1
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Qiu Z, Han Y, Noori K, Chen Z, Kashchenko M, Lin L, Olsen T, Li J, Fang H, Lyu P, Telychko M, Gu X, Adam S, Quek SY, Rodin A, Castro Neto AH, Novoselov KS, Lu J. Evidence for electron-hole crystals in a Mott insulator. NATURE MATERIALS 2024; 23:1055-1062. [PMID: 38831130 DOI: 10.1038/s41563-024-01910-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 04/30/2024] [Indexed: 06/05/2024]
Abstract
The coexistence of correlated electron and hole crystals enables the realization of quantum excitonic states, capable of hosting counterflow superfluidity and topological orders with long-range quantum entanglement. Here we report evidence for imbalanced electron-hole crystals in a doped Mott insulator, namely, α-RuCl3, through gate-tunable non-invasive van der Waals doping from graphene. Real-space imaging via scanning tunnelling microscopy reveals two distinct charge orderings at the lower and upper Hubbard band energies, whose origin is attributed to the correlation-driven honeycomb hole crystal composed of hole-rich Ru sites and rotational-symmetry-breaking paired electron crystal composed of electron-rich Ru-Ru bonds, respectively. Moreover, a gate-induced transition of electron-hole crystals is directly visualized, further corroborating their nature as correlation-driven charge crystals. The realization and atom-resolved visualization of imbalanced electron-hole crystals in a doped Mott insulator opens new doors in the search for correlated bosonic states within strongly correlated materials.
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Affiliation(s)
- Zhizhan Qiu
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore, Singapore
| | - Yixuan Han
- Department of Chemistry, National University of Singapore, Singapore, Singapore
| | - Keian Noori
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore, Singapore
- Centre for Advanced 2D Materials (CA2DM), National University of Singapore, Singapore, Singapore
| | - Zhaolong Chen
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore, Singapore
- School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen, China
| | - Mikhail Kashchenko
- Programmable Functional Materials Lab, Brain and Consciousness Research Center, Moscow, Russia
- Center for Photonics and 2D Materials, Moscow Institute of Physics and Technology, Dolgoprudny, Russia
| | - Li Lin
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore, Singapore
- School of Materials Science and Engineering, Peking University, Beijing, China
| | - Thomas Olsen
- CAMD, Department of Physics, Technical university of Denmark, Lyngby, Denmark
| | - Jing Li
- School of Chemistry, Beihang University, Beijing, China
| | - Hanyan Fang
- Department of Chemistry, National University of Singapore, Singapore, Singapore
| | - Pin Lyu
- Department of Chemistry, National University of Singapore, Singapore, Singapore
| | - Mykola Telychko
- Department of Chemistry, National University of Singapore, Singapore, Singapore
| | - Xingyu Gu
- Centre for Advanced 2D Materials (CA2DM), National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
| | - Shaffique Adam
- Centre for Advanced 2D Materials (CA2DM), National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
- Yale-NUS College, Singapore, Singapore
- Department of Materials Science & Engineering, National University of Singapore, Singapore, Singapore
| | - Su Ying Quek
- Centre for Advanced 2D Materials (CA2DM), National University of Singapore, Singapore, Singapore
- Department of Physics, National University of Singapore, Singapore, Singapore
- Department of Materials Science & Engineering, National University of Singapore, Singapore, Singapore
- NUS Graduate School, Integrative Sciences and Engineering Programme, National University of Singapore, Singapore, Singapore
| | - Aleksandr Rodin
- Centre for Advanced 2D Materials (CA2DM), National University of Singapore, Singapore, Singapore
- Yale-NUS College, Singapore, Singapore
| | - A H Castro Neto
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore, Singapore
- Centre for Advanced 2D Materials (CA2DM), National University of Singapore, Singapore, Singapore
- Department of Materials Science & Engineering, National University of Singapore, Singapore, Singapore
| | - Kostya S Novoselov
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore, Singapore.
- Department of Materials Science & Engineering, National University of Singapore, Singapore, Singapore.
| | - Jiong Lu
- Institute for Functional Intelligent Materials, National University of Singapore, Singapore, Singapore.
- Department of Chemistry, National University of Singapore, Singapore, Singapore.
- Centre for Advanced 2D Materials (CA2DM), National University of Singapore, Singapore, Singapore.
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2
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Pack J, Guo Y, Liu Z, Jessen BS, Holtzman L, Liu S, Cothrine M, Watanabe K, Taniguchi T, Mandrus DG, Barmak K, Hone J, Dean CR. Charge-transfer contacts for the measurement of correlated states in high-mobility WSe 2. NATURE NANOTECHNOLOGY 2024; 19:948-954. [PMID: 39054388 DOI: 10.1038/s41565-024-01702-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 05/22/2024] [Indexed: 07/27/2024]
Abstract
Two-dimensional semiconductors, such as transition metal dichalcogenides, have demonstrated tremendous promise for the development of highly tunable quantum devices. Realizing this potential requires low-resistance electrical contacts that perform well at low temperatures and low densities where quantum properties are relevant. Here we present a new device architecture for two-dimensional semiconductors that utilizes a charge-transfer layer to achieve large hole doping in the contact region, and implement this technique to measure the magnetotransport properties of high-purity monolayer WSe2. We measure a record-high hole mobility of 80,000 cm2 V-1 s-1 and access channel carrier densities as low as 1.6 × 1011 cm-2, an order of magnitude lower than previously achievable. Our ability to realize transparent contact to high-mobility devices at low density enables transport measurements of correlation-driven quantum phases including the observation of a low-temperature metal-insulator transition in a density and temperature regime where Wigner crystal formation is expected and the observation of the fractional quantum Hall effect under large magnetic fields. The charge-transfer contact scheme enables the discovery and manipulation of new quantum phenomena in two-dimensional semiconductors and their heterostructures.
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Affiliation(s)
- Jordan Pack
- Department of Physics, Columbia University, New York, NY, USA
| | - Yinjie Guo
- Department of Physics, Columbia University, New York, NY, USA
| | - Ziyu Liu
- Department of Physics, Columbia University, New York, NY, USA
| | - Bjarke S Jessen
- Department of Physics, Columbia University, New York, NY, USA
| | - Luke Holtzman
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, US
| | - Song Liu
- Department of Mechanical Engineering, Columbia University, New York, NY, USA
| | - Matthew Cothrine
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, US
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - David G Mandrus
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, US
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, US
| | - Katayun Barmak
- Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, US
| | - James Hone
- Department of Mechanical Engineering, Columbia University, New York, NY, USA
| | - Cory R Dean
- Department of Physics, Columbia University, New York, NY, USA.
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3
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Li H, Xiang Z, Wang T, Naik MH, Kim W, Nie J, Li S, Ge Z, He Z, Ou Y, Banerjee R, Taniguchi T, Watanabe K, Tongay S, Zettl A, Louie SG, Zaletel MP, Crommie MF, Wang F. Imaging tunable Luttinger liquid systems in van der Waals heterostructures. Nature 2024; 631:765-770. [PMID: 38961296 DOI: 10.1038/s41586-024-07596-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2023] [Accepted: 05/23/2024] [Indexed: 07/05/2024]
Abstract
One-dimensional (1D) interacting electrons are often described as a Luttinger liquid1-4 having properties that are intrinsically different from those of Fermi liquids in higher dimensions5,6. In materials systems, 1D electrons exhibit exotic quantum phenomena that can be tuned by both intra- and inter-1D-chain electronic interactions, but their experimental characterization can be challenging. Here we demonstrate that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays. We have imaged the evolution of DW Luttinger liquids under different interaction regimes tuned by electron density using scanning tunnelling microscopy. Single DWs at low carrier density are highly susceptible to Wigner crystallization consistent with a spin-incoherent Luttinger liquid, whereas at intermediate densities dimerized Wigner crystals form because of an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions that gives rise to new quantum phases. At low electron densities, inter-chain interactions are dominant and induce a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase in which electrons are ordered with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures provides opportunities to explore Luttinger liquid physics.
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Affiliation(s)
- Hongyuan Li
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Graduate Group in Applied Science and Technology, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Ziyu Xiang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Graduate Group in Applied Science and Technology, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Tianle Wang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Mit H Naik
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Woochang Kim
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Jiahui Nie
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
| | - Shiyu Li
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
| | - Zhehao Ge
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
| | - Zehao He
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
| | - Yunbo Ou
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Rounak Banerjee
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Sefaattin Tongay
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Alex Zettl
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Steven G Louie
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Michael P Zaletel
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
| | - Michael F Crommie
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
- Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Feng Wang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
- Kavli Energy Nano Sciences Institute at the University of California Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
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4
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Valenti A, Calvera V, Kivelson SA, Berg E, Huber SD. Nematic Metal in a Multivalley Electron Gas: Variational Monte Carlo Analysis and Application to AlAs. PHYSICAL REVIEW LETTERS 2024; 132:266501. [PMID: 38996276 DOI: 10.1103/physrevlett.132.266501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Revised: 01/17/2024] [Accepted: 04/26/2024] [Indexed: 07/14/2024]
Abstract
The two-dimensional electron gas is of fundamental importance in quantum many-body physics. We study a minimal extension of this model with C_{4} (as opposed to full rotational) symmetry and an electronic dispersion with two valleys with anisotropic effective masses. Electrons in our model interact via Coulomb repulsion, screened by distant metallic gates. Using variational Monte Carlo simulations, we find a broad intermediate range of densities with a metallic valley-polarized, spin-unpolarized ground state. Our results are of direct relevance to the recently discovered "nematic" state in AlAs quantum wells. For the effective mass anisotropy relevant to this system, m_{x}/m_{y}≈5.2, we obtain a transition from an anisotropic metal to a valley-polarized metal at r_{s}≈12 (where r_{s} is the dimensionless Wigner-Seitz radius). At still lower densities, we find a (possibly metastable) valley and spin-polarized state with a reduced electronic anisotropy.
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5
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Zeng Y, Guerci D, Crépel V, Millis AJ, Cano J. Sublattice Structure and Topology in Spontaneously Crystallized Electronic States. PHYSICAL REVIEW LETTERS 2024; 132:236601. [PMID: 38905641 DOI: 10.1103/physrevlett.132.236601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 05/13/2024] [Accepted: 05/16/2024] [Indexed: 06/23/2024]
Abstract
The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. Here, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective "time-reversal symmetry" and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.
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6
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Vodeb J, Diego M, Vaskivskyi Y, Logaric L, Gerasimenko Y, Kabanov V, Lipovsek B, Topic M, Mihailovic D. Non-equilibrium quantum domain reconfiguration dynamics in a two-dimensional electronic crystal and a quantum annealer. Nat Commun 2024; 15:4836. [PMID: 38844460 PMCID: PMC11156939 DOI: 10.1038/s41467-024-49179-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 05/23/2024] [Indexed: 06/09/2024] Open
Abstract
Relaxation dynamics of complex many-body quantum systems trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and energy-efficient memory devices. In this work, we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material using time-resolved scanning tunneling microscopy and unveil a crossover from temperature to noisy quantum fluctuation dominated dynamics. The process is modeled using a programmable superconducting quantum annealer in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment and quantum simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics.
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Affiliation(s)
- Jaka Vodeb
- Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia.
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, Wilhelm-Johnen-Straße, 52425, Jülich, Germany.
| | - Michele Diego
- Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
| | - Yevhenii Vaskivskyi
- Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia
| | - Leonard Logaric
- Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
| | | | - Viktor Kabanov
- Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia
| | - Benjamin Lipovsek
- Faculty for Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia
| | - Marko Topic
- Faculty for Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia
| | - Dragan Mihailovic
- Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia.
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia.
- CENN Nanocenter, Jamova 39, 1000, Ljubljana, Slovenia.
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7
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Escobar Azor M, Alrakik A, de Bentzmann L, Telleria-Allika X, Sánchez de Merás A, Evangelisti S, Berger JA. The Emergence of the Hexagonal Lattice in Two-Dimensional Wigner Fragments. J Phys Chem Lett 2024; 15:3571-3575. [PMID: 38526852 DOI: 10.1021/acs.jpclett.4c00453] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/27/2024]
Abstract
At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments, we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localization in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localize are made. The density profiles we obtain emerge naturally when we minimize the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure, which has been predicted to be the ground-state structure of the two-dimensional Wigner crystal.
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Affiliation(s)
- Miguel Escobar Azor
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
- European Theoretical Spectroscopy Facility (ETSF), https://www.etsf.eu/
| | - Amer Alrakik
- Laboratoire de Chimie et Physique Quantiques, CNRS, Université de Toulouse, UPS, 118 route de Narbonne, F-31062 Toulouse, France
| | - Louan de Bentzmann
- Laboratoire de Chimie et Physique Quantiques, CNRS, Université de Toulouse, UPS, 118 route de Narbonne, F-31062 Toulouse, France
| | - Xabier Telleria-Allika
- Polimero eta Material Aurreratuak: Fisika, Kimika eta Teknologia saila, Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Spain
| | | | - Stefano Evangelisti
- Laboratoire de Chimie et Physique Quantiques, CNRS, Université de Toulouse, UPS, 118 route de Narbonne, F-31062 Toulouse, France
| | - J Arjan Berger
- Laboratoire de Chimie et Physique Quantiques, CNRS, Université de Toulouse, UPS, 118 route de Narbonne, F-31062 Toulouse, France
- European Theoretical Spectroscopy Facility (ETSF), https://www.etsf.eu/
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8
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Madathil PT, Wang C, Singh SK, Gupta A, Rosales KAV, Chung YJ, West KW, Baldwin KW, Pfeiffer LN, Engel LW, Shayegan M. Signatures of Correlated Defects in an Ultraclean Wigner Crystal in the Extreme Quantum Limit. PHYSICAL REVIEW LETTERS 2024; 132:096502. [PMID: 38489610 DOI: 10.1103/physrevlett.132.096502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Revised: 01/04/2024] [Accepted: 02/05/2024] [Indexed: 03/17/2024]
Abstract
Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the Coulomb repulsion. The nature of this exotic, many-body, quantum phase is yet to be fully understood and experimentally revealed. Here we probe one of WC's most fundamental parameters, namely, the energy gap that determines its low-temperature conductivity, in record mobility, ultrahigh-purity, two-dimensional electrons confined to GaAs quantum wells. The WC domains in these samples contain ≃1000 electrons. The measured gaps are a factor of three larger than previously reported for lower quality samples, and agree remarkably well with values predicted for the lowest-energy, intrinsic, hypercorrelated bubble defects in a WC made of flux-electron composite fermions, rather than bare electrons. The agreement is particularly noteworthy, given that the calculations are done for disorder-free composite fermion WCs, and there are no adjustable parameters. The results reflect the exceptionally high quality of the samples, and suggest that composite fermion WCs are indeed more stable compared to their electron counterparts.
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Affiliation(s)
- P T Madathil
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - C Wang
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S K Singh
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - A Gupta
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L W Engel
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - M Shayegan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
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9
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Antebi O, Stern A, Berg E. Stoner Ferromagnetism in a Momentum-Confined Interacting 2D Electron Gas. PHYSICAL REVIEW LETTERS 2024; 132:086501. [PMID: 38457700 DOI: 10.1103/physrevlett.132.086501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2023] [Revised: 11/11/2023] [Accepted: 01/19/2024] [Indexed: 03/10/2024]
Abstract
In this work we investigate the ground state of a momentum-confined interacting 2D electron gas, a momentum-space analog of an infinite quantum well. The study is performed by combining analytical results with a numerical exact diagonalization procedure. We find a ferromagnetic ground state near a particular electron density and for a range of effective electron (or hole) masses. We argue that this observation may be relevant to the generalized Stoner ferromagnetism recently observed in multilayer graphene systems. The collective magnon excitations exhibit a linear dispersion, which originates from a diverging spin stiffness.
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Affiliation(s)
- Ohad Antebi
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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10
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Yang Y, Morales MA, Zhang S. Metal-Insulator Transition in a Semiconductor Heterobilayer Model. PHYSICAL REVIEW LETTERS 2024; 132:076503. [PMID: 38427879 DOI: 10.1103/physrevlett.132.076503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 01/17/2024] [Indexed: 03/03/2024]
Abstract
Transition metal dichalcogenide superlattices provide an exciting new platform for exploring and understanding a variety of phases of matter. The moiré continuum Hamiltonian, of two-dimensional jellium in a modulating potential, provides a fundamental model for such systems. Accurate computations with this model are essential for interpreting experimental observations and making predictions for future explorations. In this work, we combine two complementary quantum Monte Carlo (QMC) methods, phaseless auxiliary field quantum Monte Carlo and fixed-phase diffusion Monte Carlo, to study the ground state of this Hamiltonian. We observe a metal-insulator transition between a paramagnet and a 120° Néel ordered state as the moiré potential depth and the interaction strength are varied. We find significant differences from existing results by Hartree-Fock and exact diagonalization studies. In addition, we benchmark density-functional theory, and suggest an optimal hybrid functional which best approximates our QMC results.
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Affiliation(s)
- Yubo Yang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Miguel A Morales
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Shiwei Zhang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
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11
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Bozin ES, Abeykoon M, Conradson S, Baldinozzi G, Sutar P, Mihailovic D. Crystallization of polarons through charge and spin ordering transitions in 1T-TaS 2. Nat Commun 2023; 14:7055. [PMID: 37923707 PMCID: PMC10624925 DOI: 10.1038/s41467-023-42631-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 10/16/2023] [Indexed: 11/06/2023] Open
Abstract
The interaction of electrons with the lattice in metals can lead to reduction of their kinetic energy to the point where they may form heavy, dressed quasiparticles-polarons. Unfortunately, polaronic lattice distortions are difficult to distinguish from more conventional charge- and spin-ordering phenomena at low temperatures. Here we present a study of local symmetry breaking of the lattice structure on the picosecond timescale in the prototype layered dichalcogenide Mott insulator 1T-TaS2 using X-ray pair-distribution function measurements. We clearly identify symmetry-breaking polaronic lattice distortions at temperatures well above the ordered phases, and record the evolution of broken symmetry states from 915 K to 15 K. The data imply that charge ordering is driven by polaron crystallization into a Wigner crystal-like state, rather than Fermi surface nesting or conventional electron-phonon coupling. At intermediate temperatures the local lattice distortions are found to be consistent with a quantum spin liquid state.
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Affiliation(s)
- E S Bozin
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, USA.
| | - M Abeykoon
- Photon Sciences Division, Brookhaven National Laboratory, Upton, NY, USA
| | - S Conradson
- Dept. of Complex Matter, Jozef Stefan Institute, Ljubljana, Slovenia
| | - G Baldinozzi
- Centralesupélec, CNRS, SPMS, Université Paris-Saclay, bât Eiffel, Gif-sur-Yvette, Île-de-France, France
| | - P Sutar
- Dept. of Complex Matter, Jozef Stefan Institute, Ljubljana, Slovenia
| | - D Mihailovic
- Dept. of Complex Matter, Jozef Stefan Institute, Ljubljana, Slovenia.
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12
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Lu X, Zhang S, Wang Y, Gao X, Yang K, Guo Z, Gao Y, Ye Y, Han Z, Liu J. Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures. Nat Commun 2023; 14:5550. [PMID: 37689704 PMCID: PMC10492827 DOI: 10.1038/s41467-023-41293-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Accepted: 08/29/2023] [Indexed: 09/11/2023] Open
Abstract
Graphene has aroused great attention due to the intriguing properties associated with its low-energy Dirac Hamiltonian. When graphene is coupled with a correlated insulating substrate, electronic states that cannot be revealed in either individual layer may emerge in a synergistic manner. Here, we theoretically study the correlated and topological states in Coulomb-coupled and gate-tunable graphene-insulator heterostructures. By electrostatically aligning the electronic bands, charge carriers transferred between graphene and the insulator can yield a long-wavelength electronic crystal at the interface, exerting a superlattice Coulomb potential on graphene and generating topologically nontrivial subbands. This coupling can further boost electron-electron interaction effects in graphene, leading to a spontaneous bandgap formation at the Dirac point and interaction-enhanced Fermi velocity. Reciprocally, the electronic crystal at the interface is substantially stabilized with the help of cooperative interlayer Coulomb coupling. We propose a number of substrate candidates for graphene to experimentally demonstrate these effects.
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Affiliation(s)
- Xin Lu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Shihao Zhang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Yaning Wang
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China
| | - Xiang Gao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, 030006, Taiyuan, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, China
| | - Kaining Yang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, 030006, Taiyuan, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, China
| | - Zhongqing Guo
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Yuchen Gao
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China
- State Key Lab for Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing, 100871, China
| | - Yu Ye
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China
- State Key Lab for Mesoscopic Physics and Frontiers Science Center for Nano-Optoelectronics, School of Physics, Peking University, Beijing, 100871, China
| | - Zheng Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, 030006, Taiyuan, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, China
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China.
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, 201210, China.
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13
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Kim KS, Murthy C, Pandey A, Kivelson SA. Interstitial-Induced Ferromagnetism in a Two-Dimensional Wigner Crystal. PHYSICAL REVIEW LETTERS 2022; 129:227202. [PMID: 36493455 DOI: 10.1103/physrevlett.129.227202] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2022] [Accepted: 10/27/2022] [Indexed: 06/17/2023]
Abstract
The two-dimensional Wigner crystal (WC) occurs in the strongly interacting regime (r_{s}≫1) of the two-dimensional electron gas (2DEG). The magnetism of a pure WC is determined by tunneling processes that induce multispin ring-exchange interactions, resulting in fully polarized ferromagnetism for large enough r_{s}. Recently, Hossain et al. [Proc. Natl. Acad. Sci. U.S.A. 117, 32244 (2020)PNASA60027-842410.1073/pnas.2018248117] reported the occurrence of a fully polarized ferromagnetic insulator at r_{s}≳35 in an AlAs quantum well, but at temperatures orders of magnitude larger than the predicted exchange energies for the pure WC. Here, we analyze the large r_{s} dynamics of an interstitial defect in the WC, and show that it produces local ferromagnetism with much higher energy scales. Three hopping processes are dominant, which favor a large, fully polarized ferromagnetic polaron. Based on the above results, we speculate concerning the phenomenology of the magnetism near the metal-insulator transition of the 2DEG.
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Affiliation(s)
- Kyung-Su Kim
- Department of Physics, Stanford University, Stanford, California 93405, USA
| | - Chaitanya Murthy
- Department of Physics, Stanford University, Stanford, California 93405, USA
| | - Akshat Pandey
- Department of Physics, Stanford University, Stanford, California 93405, USA
| | - Steven A Kivelson
- Department of Physics, Stanford University, Stanford, California 93405, USA
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14
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Tunable quantum criticalities in an isospin extended Hubbard model simulator. Nature 2022; 609:479-484. [PMID: 36104555 PMCID: PMC9477744 DOI: 10.1038/s41586-022-05106-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 07/13/2022] [Indexed: 12/01/2022]
Abstract
Studying strong electron correlations has been an essential driving force for pushing the frontiers of condensed matter physics. In particular, in the vicinity of correlation-driven quantum phase transitions (QPTs), quantum critical fluctuations of multiple degrees of freedom facilitate exotic many-body states and quantum critical behaviours beyond Landau's framework1. Recently, moiré heterostructures of van der Waals materials have been demonstrated as highly tunable quantum platforms for exploring fascinating, strongly correlated quantum physics2-22. Here we report the observation of tunable quantum criticalities in an experimental simulator of the extended Hubbard model with spin-valley isospins arising in chiral-stacked twisted double bilayer graphene (cTDBG). Scaling analysis shows a quantum two-stage criticality manifesting two distinct quantum critical points as the generalized Wigner crystal transits to a Fermi liquid by varying the displacement field, suggesting the emergence of a critical intermediate phase. The quantum two-stage criticality evolves into a quantum pseudo criticality as a high parallel magnetic field is applied. In such a pseudo criticality, we find that the quantum critical scaling is only valid above a critical temperature, indicating a weak first-order QPT therein. Our results demonstrate a highly tunable solid-state simulator with intricate interplay of multiple degrees of freedom for exploring exotic quantum critical states and behaviours.
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15
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Hossain MS, Ma MK, Villegas-Rosales KA, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Anisotropic Two-Dimensional Disordered Wigner Solid. PHYSICAL REVIEW LETTERS 2022; 129:036601. [PMID: 35905352 DOI: 10.1103/physrevlett.129.036601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2021] [Accepted: 06/07/2022] [Indexed: 06/15/2023]
Abstract
The interplay between the Fermi sea anisotropy, electron-electron interaction, and localization phenomena can give rise to exotic many-body phases. An exciting example is an anisotropic two-dimensional (2D) Wigner solid (WS), where electrons form an ordered array with an anisotropic lattice structure. Such a state has eluded experiments up to now as its realization is extremely demanding: First, a WS entails very low densities where the Coulomb interaction dominates over the kinetic (Fermi) energy. Attaining such low densities while keeping the disorder low is very challenging. Second, the low-density requirement has to be fulfilled in a material that hosts an anisotropic Fermi sea. Here, we report transport measurements in a clean (low-disorder) 2D electron system with anisotropic effective mass and Fermi sea. The data reveal that at extremely low electron densities, when the r_{s} parameter, the ratio of the Coulomb to the Fermi energy, exceeds ≃38, the current-voltage characteristics become strongly nonlinear at small dc biases. Several key features of the nonlinear characteristics, including their anisotropic voltage thresholds, are consistent with the formation of a disordered, anisotropic WS pinned by the ubiquitous disorder potential.
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Affiliation(s)
- Md S Hossain
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M K Ma
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas-Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
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16
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Wang QH, Bedoya-Pinto A, Blei M, Dismukes AH, Hamo A, Jenkins S, Koperski M, Liu Y, Sun QC, Telford EJ, Kim HH, Augustin M, Vool U, Yin JX, Li LH, Falin A, Dean CR, Casanova F, Evans RFL, Chshiev M, Mishchenko A, Petrovic C, He R, Zhao L, Tsen AW, Gerardot BD, Brotons-Gisbert M, Guguchia Z, Roy X, Tongay S, Wang Z, Hasan MZ, Wrachtrup J, Yacoby A, Fert A, Parkin S, Novoselov KS, Dai P, Balicas L, Santos EJG. The Magnetic Genome of Two-Dimensional van der Waals Materials. ACS NANO 2022; 16:6960-7079. [PMID: 35442017 PMCID: PMC9134533 DOI: 10.1021/acsnano.1c09150] [Citation(s) in RCA: 70] [Impact Index Per Article: 35.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 02/23/2022] [Indexed: 05/23/2023]
Abstract
Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.
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Affiliation(s)
- Qing Hua Wang
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Amilcar Bedoya-Pinto
- NISE
Department, Max Planck Institute of Microstructure
Physics, 06120 Halle, Germany
- Instituto
de Ciencia Molecular (ICMol), Universitat
de València, 46980 Paterna, Spain
| | - Mark Blei
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Avalon H. Dismukes
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Assaf Hamo
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Sarah Jenkins
- Twist
Group,
Faculty of Physics, University of Duisburg-Essen, Campus Duisburg, 47057 Duisburg, Germany
| | - Maciej Koperski
- Institute
for Functional Intelligent Materials, National
University of Singapore, 117544 Singapore
| | - Yu Liu
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Qi-Chao Sun
- Physikalisches
Institut, University of Stuttgart, 70569 Stuttgart, Germany
| | - Evan J. Telford
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
- Department
of Physics, Columbia University, New York, New York 10027, United States
| | - Hyun Ho Kim
- School
of Materials Science and Engineering, Department of Energy Engineering
Convergence, Kumoh National Institute of
Technology, Gumi 39177, Korea
| | - Mathias Augustin
- Institute
for Condensed Matter Physics and Complex Systems, School of Physics
and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
| | - Uri Vool
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- John Harvard
Distinguished Science Fellows Program, Harvard
University, Cambridge, Massachusetts 02138, United States
| | - Jia-Xin Yin
- Laboratory
for Topological Quantum Matter and Spectroscopy, Department of Physics, Princeton University, Princeton, New Jersey 08544, United States
| | - Lu Hua Li
- Institute
for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Victoria 3216, Australia
| | - Alexey Falin
- Institute
for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Victoria 3216, Australia
| | - Cory R. Dean
- Department
of Physics, Columbia University, New York, New York 10027, United States
| | - Fèlix Casanova
- CIC nanoGUNE
BRTA, 20018 Donostia - San Sebastián, Basque
Country, Spain
- IKERBASQUE,
Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
| | - Richard F. L. Evans
- Department
of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
| | - Mairbek Chshiev
- Université
Grenoble Alpes, CEA, CNRS, Spintec, 38000 Grenoble, France
- Institut
Universitaire de France, 75231 Paris, France
| | - Artem Mishchenko
- Department
of Physics and Astronomy, University of
Manchester, Manchester, M13 9PL, United Kingdom
- National
Graphene Institute, University of Manchester, Manchester, M13 9PL, United Kingdom
| | - Cedomir Petrovic
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Rui He
- Department
of Electrical and Computer Engineering, Texas Tech University, 910 Boston Avenue, Lubbock, Texas 79409, United
States
| | - Liuyan Zhao
- Department
of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, United States
| | - Adam W. Tsen
- Institute
for Quantum Computing and Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Brian D. Gerardot
- SUPA, Institute
of Photonics and Quantum Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, United Kingdom
| | - Mauro Brotons-Gisbert
- SUPA, Institute
of Photonics and Quantum Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, United Kingdom
| | - Zurab Guguchia
- Laboratory
for Muon Spin Spectroscopy, Paul Scherrer
Institute, CH-5232 Villigen PSI, Switzerland
| | - Xavier Roy
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sefaattin Tongay
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Ziwei Wang
- Department
of Physics and Astronomy, University of
Manchester, Manchester, M13 9PL, United Kingdom
- National
Graphene Institute, University of Manchester, Manchester, M13 9PL, United Kingdom
| | - M. Zahid Hasan
- Materials
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Princeton
Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States
- National
High Magnetic Field Laboratory, Florida
State University, Tallahassee, Florida 32310, United States
| | - Joerg Wrachtrup
- Physikalisches
Institut, University of Stuttgart, 70569 Stuttgart, Germany
- Max Planck
Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Amir Yacoby
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- John A.
Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Albert Fert
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
- Unité
Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
- Department
of Materials Physics UPV/EHU, 20018 Donostia - San Sebastián, Basque Country, Spain
| | - Stuart Parkin
- NISE
Department, Max Planck Institute of Microstructure
Physics, 06120 Halle, Germany
| | - Kostya S. Novoselov
- Institute
for Functional Intelligent Materials, National
University of Singapore, 117544 Singapore
| | - Pengcheng Dai
- Department
of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Luis Balicas
- National
High Magnetic Field Laboratory, Florida
State University, Tallahassee, Florida 32310, United States
- Department
of Physics, Florida State University, Tallahassee, Florida 32306, United States
| | - Elton J. G. Santos
- Institute
for Condensed Matter Physics and Complex Systems, School of Physics
and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
- Higgs Centre
for Theoretical Physics, The University
of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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17
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Ashoori R. A long-sought regime of electronic behaviour. NATURE MATERIALS 2022; 21:268-269. [PMID: 35241820 DOI: 10.1038/s41563-022-01212-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Affiliation(s)
- Raymond Ashoori
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
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18
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Falson J, Sodemann I, Skinner B, Tabrea D, Kozuka Y, Tsukazaki A, Kawasaki M, von Klitzing K, Smet JH. Competing correlated states around the zero-field Wigner crystallization transition of electrons in two dimensions. NATURE MATERIALS 2022; 21:311-316. [PMID: 34949813 DOI: 10.1038/s41563-021-01166-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Accepted: 11/04/2021] [Indexed: 06/14/2023]
Abstract
The competition between kinetic energy and Coulomb interactions in electronic systems leads to complex many-body ground states with competing orders. Here we present zinc oxide-based two-dimensional electron systems as a high-mobility system to study the low-temperature phases of strongly interacting electrons. An analysis of the electronic transport provides evidence for competing correlated metallic and insulating states with varying degrees of spin polarization. Some features bear quantitative resemblance to quantum Monte Carlo simulation results, including the transition point from the paramagnetic Fermi liquid to Wigner crystal and the absence of a Stoner transition. At very low temperatures, we resolve a non-monotonic spin polarizability of electrons across the phase transition, pointing towards a low spin phase of electrons, and a two-order-of-magnitude positive magnetoresistance that is challenging to understand within traditional metallic transport paradigms. This work establishes zinc oxide as a platform for studying strongly correlated electrons in two dimensions.
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Affiliation(s)
- J Falson
- Max-Planck-Institute for Solid State Research, Stuttgart, Germany.
- Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, CA, USA.
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA.
| | - I Sodemann
- Institut für Theoretische Physik, Universität Leipzig, Leipzig, Germany
- Max-Planck-Institute for the Physics of Complex Systems, Dresden, Germany
| | - B Skinner
- Department of Physics, Ohio State University, Columbus, OH, USA
| | - D Tabrea
- Max-Planck-Institute for Solid State Research, Stuttgart, Germany
| | - Y Kozuka
- Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, Tsukuba, Japan
- PRESTO, JST, Kawaguchi, Japan
| | - A Tsukazaki
- Institute for Materials Research, Tohoku University, Sendai, Japan
| | - M Kawasaki
- Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan
| | - K von Klitzing
- Max-Planck-Institute for Solid State Research, Stuttgart, Germany
| | - J H Smet
- Max-Planck-Institute for Solid State Research, Stuttgart, Germany
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19
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Brem S, Malic E. Terahertz Fingerprint of Monolayer Wigner Crystals. NANO LETTERS 2022; 22:1311-1315. [PMID: 35048702 PMCID: PMC8832488 DOI: 10.1021/acs.nanolett.1c04620] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Revised: 01/11/2022] [Indexed: 05/25/2023]
Abstract
The strong Coulomb interaction in monolayer semiconductors represents a unique opportunity for the realization of Wigner crystals without external magnetic fields. In this work, we predict that the formation of monolayer Wigner crystals can be detected by their terahertz response spectrum, which exhibits a characteristic sequence of internal optical transitions. We apply the density matrix formalism to derive the internal quantum structure and the optical conductivity of the Wigner crystal and to microscopically analyze the multipeak shape of the obtained terahertz spectrum. Moreover, we predict a characteristic shift of the peak position as a function of charge density for different atomically thin materials and show how our results can be generalized to an arbitrary two-dimensional system.
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Affiliation(s)
- Samuel Brem
- Department
of Physics, Philipps University, 35037 Marburg, Germany
| | - Ermin Malic
- Department
of Physics, Philipps University, 35037 Marburg, Germany
- Department
of Physics, Chalmers University of Technology, 41258 Göteborg, Sweden
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20
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Escobar Azor M, Alves E, Evangelisti S, Berger JA. Wigner localization in two and three dimensions: An ab initio approach. J Chem Phys 2021; 155:124114. [PMID: 34598574 DOI: 10.1063/5.0063100] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
In this work, we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function, we use a regular distribution in space of Gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach, we are able to observe the Wigner localization without ambiguity.
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Affiliation(s)
- Miguel Escobar Azor
- Laboratoire de Chimie et Physique Quantiques, CNRS, Université Toulouse III (UPS), 118 Route de Narbonne, F-31062 Toulouse, France
| | | | - Stefano Evangelisti
- Laboratoire de Chimie et Physique Quantiques, CNRS, Université Toulouse III (UPS), 118 Route de Narbonne, F-31062 Toulouse, France
| | - J Arjan Berger
- Laboratoire de Chimie et Physique Quantiques, CNRS, Université Toulouse III (UPS), 118 Route de Narbonne, F-31062 Toulouse, France
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21
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Pan H, Das Sarma S. Interaction-Driven Filling-Induced Metal-Insulator Transitions in 2D Moiré Lattices. PHYSICAL REVIEW LETTERS 2021; 127:096802. [PMID: 34506187 DOI: 10.1103/physrevlett.127.096802] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 08/02/2021] [Indexed: 06/13/2023]
Abstract
Using a realistic band structure for twisted WSe_{2} materials, we develop a theory for the interaction-driven correlated insulators to conducting metals transitions through the tuning of the filling factor around commensurate fractional fillings of the moiré unit cell in the 2D honeycomb lattice, focusing on the dominant half-filled Mott insulating state, which exists for both long- and short-range interactions. We find metallic states slightly away from half-filling, as have recently been observed experimentally. We discuss the stabilities and the magnetic properties of the resulting insulating and metallic phases, and comment on their experimental signatures. We also discuss the nature of the correlated insulator states at the rational fractional fillings.
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Affiliation(s)
- Haining Pan
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Sankar Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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22
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Ostilli M, Presilla C. Wigner Crystallization of Electrons in a One-Dimensional Lattice: A Condensation in the Space of States. PHYSICAL REVIEW LETTERS 2021; 127:040601. [PMID: 34355957 DOI: 10.1103/physrevlett.127.040601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2019] [Revised: 04/21/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
We study the ground state of a system of spinless electrons interacting through a screened Coulomb potential in a lattice ring. By using analytical arguments, we show that, when the effective interaction compares with the kinetic energy, the system forms a Wigner crystal undergoing a first-order quantum phase transition. This transition is a condensation in the space of the states and belongs to the class of quantum phase transitions discussed in [M. Ostilli and C. Presilla, J. Phys. A 54, 055005 (2021).JPAMB51751-811310.1088/1751-8121/aba144]. The transition takes place at a critical value r_{s}_{c} of the usual dimensionless parameter r_{s} (radius of the volume available to each electron divided by effective Bohr radius) for which we are able to provide rigorous lower and upper bounds. For large screening length these bounds can be expressed in a closed analytical form. Demanding Monte Carlo simulations allow to estimate r_{s}_{c}≃2.3±0.2 at lattice filling 3/10 and screening length 10 lattice constants. This value is well within the rigorous bounds 0.7≤r_{s}_{c}≤4.3. Finally, we show that if screening is removed after the thermodynamic limit has been taken, r_{s}_{c} tends to zero. In contrast, in a bare unscreened Coulomb potential, Wigner crystallization always takes place as a smooth crossover, not as a quantum phase transition.
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Affiliation(s)
- Massimo Ostilli
- Instituto de Física, Universidade Federal da Bahia, Salvador 40170-115, Brazil
| | - Carlo Presilla
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, Roma 00185, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Roma 00185, Italy
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23
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Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature 2021; 595:53-57. [PMID: 34194018 DOI: 10.1038/s41586-021-03590-4] [Citation(s) in RCA: 54] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 04/28/2021] [Indexed: 11/09/2022]
Abstract
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two-dimensional systems are predicted to spontaneously break continuous-translation symmetry and form a quantum crystal1. Efforts to observe2-12 this elusive state of matter, termed a Wigner crystal, in two-dimensional extended systems have primarily focused on conductivity measurements on electrons confined to a single Landau level at high magnetic fields. Here we use optical spectroscopy to demonstrate that electrons in a monolayer semiconductor with density lower than 3 × 1011 per centimetre squared form a Wigner crystal. The combination of a high electron effective mass and reduced dielectric screening enables us to observe electronic charge order even in the absence of a moiré potential or an external magnetic field. The interactions between a resonantly injected exciton and electrons arranged in a periodic lattice modify the exciton bandstructure so that an umklapp resonance arises in the optical reflection spectrum, heralding the presence of charge order13. Our findings demonstrate that charge-tunable transition metal dichalcogenide monolayers14 enable the investigation of previously uncharted territory for many-body physics where interaction energy dominates over kinetic energy.
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Hossain MS, Ma MK, Rosales KAV, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Observation of spontaneous ferromagnetism in a two-dimensional electron system. Proc Natl Acad Sci U S A 2020; 117:32244-32250. [PMID: 33273119 PMCID: PMC7768770 DOI: 10.1073/pnas.2018248117] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should exceed the enhancement in the kinetic (Fermi) energy, leading to a (Bloch) ferromagnetic transition. At even lower densities, another transition to a (Wigner) solid, an ordered array of electrons, should occur. Experimental access to these regimes, however, has been limited because of the absence of a material platform that supports an electron system with very high quality (low disorder) and low density simultaneously. Here we explore the ground states of interacting electrons in an exceptionally clean, two-dimensional electron system confined to a modulation-doped AlAs quantum well. The large electron effective mass in this system allows us to reach very large values of the interaction parameter [Formula: see text], defined as the ratio of the Coulomb to Fermi energies. As we lower the electron density via gate bias, we find a sequence of phases, qualitatively consistent with the above scenario: a paramagnetic phase at large densities, a spontaneous transition to a ferromagnetic state when [Formula: see text] surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when [Formula: see text] exceeds [Formula: see text] However, our sample makes a transition to an insulating state at [Formula: see text], preceding the onset of the spontaneous ferromagnetism, implying that besides interaction, the role of disorder must also be taken into account in understanding the different phases of a realistic dilute electron system.
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Affiliation(s)
- M S Hossain
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - M K Ma
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | | | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544
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Holzmann M, Moroni S. Itinerant-Electron Magnetism: The Importance of Many-Body Correlations. PHYSICAL REVIEW LETTERS 2020; 124:206404. [PMID: 32501090 DOI: 10.1103/physrevlett.124.206404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Accepted: 05/05/2020] [Indexed: 06/11/2023]
Abstract
Do electrons become ferromagnetic just because of their repulsive Coulomb interaction? Our calculations on the three-dimensional electron gas imply that itinerant ferromagnetism of delocalized electrons without lattice and band structure, the most basic model considered by Stoner, is suppressed due to many-body correlations as speculated already by Wigner, and a possible ferromagnetic transition lowering the density is precluded by the formation of the Wigner crystal.
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Affiliation(s)
- Markus Holzmann
- Univ. Grenoble Alpes, CNRS, LPMMC, 38000 Grenoble, France and Institut Laue Langevin, BP 156, F-38042 Grenoble Cedex 9, France
| | - Saverio Moroni
- CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali, and SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy
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Liu E, van Baren J, Taniguchi T, Watanabe K, Chang YC, Lui CH. Landau-Quantized Excitonic Absorption and Luminescence in a Monolayer Valley Semiconductor. PHYSICAL REVIEW LETTERS 2020; 124:097401. [PMID: 32202881 DOI: 10.1103/physrevlett.124.097401] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2019] [Revised: 10/09/2019] [Accepted: 01/17/2020] [Indexed: 06/10/2023]
Abstract
We investigate Landau-quantized excitonic absorption and luminescence of monolayer WSe_{2} under magnetic field. We observe gate-dependent quantum oscillations in the bright exciton and trions (or exciton polarons) as well as the dark trions and their phonon replicas. Our results reveal spin- and valley-polarized Landau levels (LLs) with filling factors n=+0, +1 in the bottom conduction band and n=-0 to -6 in the top valence band, including the Berry-curvature-induced n=±0 LLs of massive Dirac fermions. The LL filling produces periodic plateaus in the exciton energy shift accompanied by sharp oscillations in the exciton absorption width and magnitude. This peculiar exciton behavior can be simulated by semiempirical calculations. The experimentally deduced g factors of the conduction band (g∼2.5) and valence band (g∼15) exceed those predicted in a single-particle model (g=1.5, 5.5, respectively). Such g-factor enhancement implies strong many-body interactions in gated monolayer WSe_{2}. The complex interplay between Landau quantization, excitonic effects, and many-body interactions makes monolayer WSe_{2} a promising platform to explore novel correlated quantum phenomena.
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Affiliation(s)
- Erfu Liu
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Jeremiah van Baren
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Takashi Taniguchi
- National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Ibaraki 305-004, Japan
| | - Yia-Chung Chang
- Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan
| | - Chun Hung Lui
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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Lubchenko V, Kurnosov A. Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids. J Chem Phys 2019; 150:244502. [PMID: 31255083 DOI: 10.1063/1.5063587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a microscopic picture rationalizing the surprisingly steep decrease in the bandgap with temperature in insulators, crystalline or otherwise. The gap narrowing largely results from fluctuations of long-wavelength optical phonons-when the latter are present-or their disordered analogs if the material is amorphous. We elaborate on this notion to show that possibly with the exception of weakly bound solids made of closed-shell electronic configurations, the existence of an insulating gap or pseudogap in a periodic solid implies that optical phonons must be present, too. This means that in an insulating solid, the primitive cell must have at least two atoms and/or that a charge density wave is present, with the possible exception of weakly bonded solids such as rare-gas or ferromagnetic Wigner crystals. As a corollary, a (periodic) elemental solid held together by nonclosed shell interactions and whose primitive unit contains only one atom will ordinarily be a metal, consistent with observation. Consequences of the present picture for Wigner solids are discussed. A simple field theory of the metal-insulator transition is constructed that directly ties long-wavelength optical vibrations with fluctuations of an order parameter for the metal-insulator transition. The order parameter is shown to have at least two components, yet no Goldstone mode arises as a result of the transition.
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Affiliation(s)
- Vassiliy Lubchenko
- Department of Chemistry, University of Houston, Houston, Texas 77204-5003, USA
| | - Arkady Kurnosov
- Department of Chemistry, University of Houston, Houston, Texas 77204-5003, USA
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Lewis AM, Berkelbach TC. Ab Initio Lifetime and Concomitant Double-Excitation Character of Plasmons at Metallic Densities. PHYSICAL REVIEW LETTERS 2019; 122:226402. [PMID: 31283277 DOI: 10.1103/physrevlett.122.226402] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Indexed: 06/09/2023]
Abstract
The accurate calculation of excited state properties of interacting electrons in the condensed phase is an immense challenge in computational physics. Here, we use state-of-the-art equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) to calculate the dynamic structure factor, which can be experimentally measured by inelastic x-ray and electron scattering. Our calculations are performed on the uniform electron gas at densities corresponding to Wigner-Seitz radii of r_{s}=5, 4, and 3 corresponding to the valence electron densities of common metals. We compare our results to those obtained using the random-phase approximation (RPA), which is known to provide a reasonable description of the collective plasmon excitation and which resums only a small subset of the polarizability diagrams included in EOM-CCSD. We find that EOM-CCSD, instead of providing a perturbative improvement on the RPA plasmon, predicts a many-state plasmon resonance, where each contributing state has a double-excitation character of 80% or more. This finding amounts to an ab initio treatment of the plasmon linewidth, which is in good quantitative agreement with previous diagrammatic calculations, and highlights the strongly correlated nature of lifetime effects in condensed-phase electronic structure theory.
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Affiliation(s)
- Alan M Lewis
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027 USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
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New Reentrant Insulating Phases in Strongly Interacting 2D Systems with Low Disorder. APPLIED SCIENCES-BASEL 2018. [DOI: 10.3390/app8101909] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The metal-insulator transition (MIT) in two-dimension (2D) was discovered by Kravchenko et al. more than two decades ago in strongly interacting 2D electrons residing in a Si-metal-oxide-semiconductor field-effect transistor (Si-MOSFET). Its origin remains unresolved. Recently, low magnetic field reentrant insulating phases (RIPs), which dwell between the zero-field (B = 0) metallic state and the integer quantum Hall (QH) states where the Landau-level filling factor υ > 1, have been observed in strongly correlated 2D GaAs hole systems with a large interaction parameter, rs, (~20–40) and a high purity. A new complex phase diagram was proposed, which includes zero-field MIT, low magnetic field RIPs, integer QH states, fractional QH states, high field RIPs and insulating phases (HFIPs) with υ < 1 in which the insulating phases are explained by the formation of a Wigner crystal. Furthermore, evidence of new intermediate phases was reported. This review article serves the purpose of summarizing those recent experimental findings and theoretical endeavors to foster future research efforts.
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Sharma RO, Saini LK, Bahuguna BP. Phase diagram of a symmetric electron-hole bilayer system: a variational Monte Carlo study. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:185404. [PMID: 29557791 DOI: 10.1088/1361-648x/aab81c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the phase diagram of a symmetric electron-hole bilayer system at absolute zero temperature and in zero magnetic field within the quantum Monte Carlo approach. In particular, we conduct variational Monte Carlo simulations for various phases, i.e. the paramagnetic fluid phase, the ferromagnetic fluid phase, the anti-ferromagnetic Wigner crystal phase, the ferromagnetic Wigner crystal phase and the excitonic phase, to estimate the ground-state energy at different values of in-layer density and inter-layer spacing. Slater-Jastrow style trial wave functions, with single-particle orbitals appropriate for different phases, are used to construct the phase diagram in the (r s , d) plane by finding the relative stability of trial wave functions. At very small layer separations, we find that the fluid phases are stable, with the paramagnetic fluid phase being particularly stable at [Formula: see text] and the ferromagnetic fluid phase being particularly stable at [Formula: see text]. As the layer spacing increases, we first find that there is a phase transition from the ferromagnetic fluid phase to the ferromagnetic Wigner crystal phase when d reaches 0.4 a.u. at r s = 20, and before there is a return to the ferromagnetic fluid phase when d approaches 1 a.u. However, for r s < 20 and [Formula: see text] a.u., the excitonic phase is found to be stable. We do not find that the anti-ferromagnetic Wigner crystal is stable over the considered range of r s and d. We also find that as r s increases, the critical layer separations for Wigner crystallization increase.
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Affiliation(s)
- Rajesh O Sharma
- Applied Physics Department, Sardar Vallabhbhai National Institute of Technology Surat-395007, Gujarat, India
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Affiliation(s)
- Fergus J. M. Rogers
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
| | - Pierre-François Loos
- Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia
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Loos P, Gill PMW. The uniform electron gas. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1257] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
| | - Peter M. W. Gill
- Research School of Chemistry Australian National University Canberra Australia
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Loos PF, Ball CJ, Gill PMW. Uniform electron gases. II. The generalized local density approximation in one dimension. J Chem Phys 2014; 140:18A524. [DOI: 10.1063/1.4867910] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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López Ríos P, Seth P, Drummond ND, Needs RJ. Framework for constructing generic Jastrow correlation factors. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:036703. [PMID: 23031049 DOI: 10.1103/physreve.86.036703] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2012] [Indexed: 06/01/2023]
Abstract
We have developed a flexible framework for constructing Jastrow factors which allows for the introduction of terms involving arbitrary numbers of particles. The use of various three- and four-body Jastrow terms in quantum Monte Carlo calculations is investigated, including a four-body van der Waals-like term, and anisotropic terms. We have tested these Jastrow factors on one- and two-dimensional homogeneous electron gases, the Be, B, and O atoms, and the BeH, H2O, N2, and H2 molecules. Our optimized Jastrow factors retrieve more than 90% of the fixed-node diffusion Monte Carlo correlation energy in variational Monte Carlo for each system studied.
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Affiliation(s)
- P López Ríos
- Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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36
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Shepherd JJ, Booth GH, Alavi A. Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models. J Chem Phys 2012; 136:244101. [DOI: 10.1063/1.4720076] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
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37
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Qiu RLJ, Gao XPA, Pfeiffer LN, West KW. Connecting the reentrant insulating phase and the zero-field metal-insulator transition in a 2D hole system. PHYSICAL REVIEW LETTERS 2012; 108:106404. [PMID: 22463433 DOI: 10.1103/physrevlett.108.106404] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2011] [Indexed: 05/31/2023]
Abstract
We present the transport and capacitance measurements of 10 nm wide GaAs quantum wells with hole densities around the critical point of the 2D metal-insulator transition (critical density p(c) down to 0.8 × 10(10)/cm2, r(s) ∼ 36). For metallic hole density p(c) < p < p(c) + 0.15 × 10(10)/cm2, a reentrant insulating phase (RIP) is observed between the ν = 1 quantum Hall state and the zero-field metallic state and it is attributed to the formation of pinned Wigner crystal. Through studying the evolution of the RIP versus 2D hole density, we show that the RIP is incompressible and continuously connected to the zero-field insulator, suggesting a similar origin for these two phases.
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Affiliation(s)
- R L J Qiu
- Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, USA
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Badinski A, Haynes PD, Trail JR, Needs RJ. Methods for calculating forces within quantum Monte Carlo simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:074202. [PMID: 21386380 DOI: 10.1088/0953-8984/22/7/074202] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Atomic force calculations within the variational and diffusion quantum Monte Carlo methods are described. The advantages of calculating diffusion quantum Monte Carlo forces with the 'pure' rather than the 'mixed' probability distribution are discussed. An accurate and practical method for calculating forces using the pure distribution is presented and tested for the SiH molecule. The statistics of force estimators are explored and violations of the central limit theorem are found in some cases.
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Affiliation(s)
- A Badinski
- Theory of Condensed Matter Group, Cavendish Laboratory, Cambridge CB3 0HE, UK
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40
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Needs RJ, Towler MD, Drummond ND, López Ríos P. Continuum variational and diffusion quantum Monte Carlo calculations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:023201. [PMID: 21386247 DOI: 10.1088/0953-8984/22/2/023201] [Citation(s) in RCA: 163] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wavefunctions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well suited to implementation on petascale computers, and the computational cost scales as a polynomial in the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimization of wavefunctions, performing calculations under periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.
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Affiliation(s)
- R J Needs
- Theory of Condensed Matter Group, Cavendish Laboratory, Cambridge CB3 0HE, UK
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Gori-Giorgi P, Seidl M. Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry. Phys Chem Chem Phys 2010; 12:14405-19. [DOI: 10.1039/c0cp01061h] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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