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Li T, Li N, Guo M, Wu YJ. Phase- and temperature-driven chiral topological superfluids on a honeycomb lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:375601. [PMID: 38814243 DOI: 10.1088/1361-648x/ad51fa] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2024] [Accepted: 05/28/2024] [Indexed: 05/31/2024]
Abstract
The correlated spinful Haldane model exhibits rich topological phases consisting of chiral topological superfluids (TSFs) and topological spin density waves. However, most of previous studies mainly focus on the case with the fixed hopping phase or at zero temperature. In this paper, we study the attractive spinful Haldane model with arbitrary phase at finite temperature. The chiral TSFs with Chern numberC = 2 and 4 emerge driven by the phase and temperature. In particular, the temperature can drive aC = 2 topological superfluid from a trivial normal insulator phase at an appropriate interaction. The bulk topology of all TSFs is uncovered by the Wilson loop method, and confirmed by the responses of edge dislocations.
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Affiliation(s)
- Tong Li
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
| | - Ning Li
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
| | - Miaodi Guo
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
| | - Ya-Jie Wu
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
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2
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Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling. ATOMS 2020. [DOI: 10.3390/atoms8030058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Motivated by recent developments in the experimental study of ultracold atoms in graphene-like honeycomb optical lattices, we investigate superconductivity of the attractive Kane-Mele-Habbard (KMH) model with the next-nearest-neighbor (NNN) hoping at half filling. The mean-field approximation is used to study the phase diagram which interpolates the trivial and the non-trivial topological states. It is shown that: (a) when the NNN hoping is taken into account, one has to introduce two mean-field gap equations for the two sublattices, instead of a single gap when the NNN hopping is neglected, and (b) in the non-trivial topological region the phase diagram with the NNN hopping is significantly different compared to the phase diagram calculated previously, but without the NNN term. We also discuss the superconducting instability of the attractive KMH model that is driven by condensation of Cooperons.
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Peltonen TJ, Heikkilä TT. Flat-band superconductivity in periodically strained graphene: mean-field and Berezinskii-Kosterlitz-Thouless transition. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:365603. [PMID: 32315990 DOI: 10.1088/1361-648x/ab8b9d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2020] [Accepted: 04/21/2020] [Indexed: 06/11/2023]
Abstract
In the search of high-temperature superconductivity one option is to focus on increasing the density of electronic states. Here we study both the normal ands-wave superconducting state properties of periodically strained graphene, which exhibits approximate flat bands with a high density of states, with the flatness tunable by the strain profile. We generalize earlier results regarding a one-dimensional harmonic strain to arbitrary periodic strain fields, and further extend the results by calculating the superfluid weight and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperatureTBKTto determine the true transition point. By numerically solving the self-consistency equation, we find a strongly inhomogeneous superconducting order parameter, similarly to twisted bilayer graphene. In the flat-band regime the order parameter magnitude, critical chemical potential, critical temperature, superfluid weight, and BKT transition temperature are all approximately linear in the interaction strength, which suggests that high-temperature superconductivity might be feasible in this system. We especially show that by using realistic strain strengthsTBKTcan be made much larger than in twisted bilayer graphene, if using similar interaction strengths. We also calculate properties such as the local density of states that could serve as experimental fingerprints for the presented model.
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Affiliation(s)
- Teemu J Peltonen
- University of Jyväskylä, Department of Physics and Nanoscience Center, PO Box 35 (YFL), FI-40014 University of Jyväskylä, Finland
| | - Tero T Heikkilä
- University of Jyväskylä, Department of Physics and Nanoscience Center, PO Box 35 (YFL), FI-40014 University of Jyväskylä, Finland
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4
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Zhang W, Chen X, Kartashov YV, Konotop VV, Ye F. Coupling of Edge States and Topological Bragg Solitons. PHYSICAL REVIEW LETTERS 2019; 123:254103. [PMID: 31922795 DOI: 10.1103/physrevlett.123.254103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2019] [Indexed: 06/10/2023]
Abstract
The existence of the edge states at the interface between two media with different topological properties is protected by symmetry, which makes such states robust against structural defects or disorder. We show that, if a system supports more than one topological edge state at the interface, even a weak periodic deformation may scatter one edge state into another without coupling to bulk modes. This is the Bragg scattering of the edge modes, which in a topological system is highly selective, with closed bulk and backward scattering channels, even when conditions for resonant scattering are not satisfied. When such a system bears nonlinearity, Bragg scattering enables the formation of a new type of soliton-topological Bragg solitons. We report them in a spin-orbit-coupled (SOC) Bose-Einstein condensate in a homogeneous honeycomb Zeeman lattice. An interface supporting two edge states is created by two different SOCs, with the y component of the synthetic magnetic field having opposite directions at different sides of the interface. The reported Bragg solitons are found to be stable.
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Affiliation(s)
- Weifeng Zhang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, 108840, Russia
| | - Vladimir V Konotop
- Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
| | - Fangwei Ye
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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5
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Dong YM, Zheng DX, Wang J. Cooper instability generated by attractive fermion-fermion interaction in the two-dimensional semi-Dirac semimetals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:275601. [PMID: 30921787 DOI: 10.1088/1361-648x/ab142d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Cooper instability (CI) associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion-fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead CI can be generated only if the absolute strength of fermion-fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the CI at zero chemical potential, which in principle are harmful to CI although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the CI is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.
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Affiliation(s)
- Yao-Ming Dong
- Department of Physics, Tianjin University, Tianjin 300072, People's Republic of China
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6
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Chen C, Xu XY, Meng ZY, Hohenadler M. Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons. PHYSICAL REVIEW LETTERS 2019; 122:077601. [PMID: 30848656 DOI: 10.1103/physrevlett.122.077601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Indexed: 06/09/2023]
Abstract
The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling.
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Affiliation(s)
- Chuang Chen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Xiao Yan Xu
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Zi Yang Meng
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center of Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Martin Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
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7
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Roy B, Juričić V. Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials. PHYSICAL REVIEW LETTERS 2018; 121:137601. [PMID: 30312062 DOI: 10.1103/physrevlett.121.137601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Indexed: 06/08/2023]
Abstract
Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.
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Affiliation(s)
- Bitan Roy
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Vladimir Juričić
- Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
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8
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Umucalılar RO, Iskin M. BCS Theory of Time-Reversal-Symmetric Hofstadter-Hubbard Model. PHYSICAL REVIEW LETTERS 2017; 119:085301. [PMID: 28952771 DOI: 10.1103/physrevlett.119.085301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Indexed: 06/07/2023]
Abstract
The competition between the length scales associated with the periodicity of a lattice potential and the cyclotron radius of a uniform magnetic field is known to have dramatic effects on the single-particle properties of a quantum particle, e.g., the fractal spectrum is known as the Hofstadter butterfly. Having this intricate competition in mind, we consider a two-component Fermi gas on a square optical lattice with opposite synthetic magnetic fields for the components, and study its effects on the many-body BCS-pairing phenomenon. By a careful addressing of the distinct superfluid transitions from the semimetal, quantum spin-Hall insulator, or normal phases, we explore the low-temperature phase diagrams of the model, displaying lobe structures that are reminiscent of the well-known Mott-insulator transitions of the Bose-Hubbard model.
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Affiliation(s)
- R O Umucalılar
- Department of Physics, Koç University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey
- Department of Physics, Mimar Sinan Fine Arts University, 34380 Şişli, Istanbul, Turkey
| | - M Iskin
- Department of Physics, Koç University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey
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9
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Makino T, Katagiri Y, Ohata C, Nomura K, Haruyama J. Anisotropic atomic-structure related anomalous Hall resistance in few-layer black phosphorus. RSC Adv 2017. [DOI: 10.1039/c7ra03600k] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Specific anisotropic-atomic-structure of atom-thin black phosphorus causes the anomalous magnetic-field dependence of the Hall resistance, which opens doors to novel quantum phenomena and innovative two-dimensional atom-thin devices.
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Affiliation(s)
- T. Makino
- Faculty of Science and Engineering
- Aoyama Gakuin University
- Sagamihara
- Japan
| | - Y. Katagiri
- Faculty of Science and Engineering
- Aoyama Gakuin University
- Sagamihara
- Japan
| | - C. Ohata
- Faculty of Science and Engineering
- Aoyama Gakuin University
- Sagamihara
- Japan
| | - K. Nomura
- Faculty of Science and Engineering
- Aoyama Gakuin University
- Sagamihara
- Japan
| | - J. Haruyama
- Institute for Solid State Physics
- The University of Tokyo
- Kashiwa
- Japan
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10
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Zheng Z, Qu C, Zou X, Zhang C. Fulde-Ferrell Superfluids without Spin Imbalance in Driven Optical Lattices. PHYSICAL REVIEW LETTERS 2016; 116:120403. [PMID: 27058062 DOI: 10.1103/physrevlett.116.120403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Indexed: 06/05/2023]
Abstract
Spin-imbalanced ultracold Fermi gases have been widely studied recently as a platform for exploring the long-sought Fulde-Ferrell-Larkin-Ovchinnikov superfluid phases, but so far conclusive evidence has not been found. Here we propose to realize an Fulde-Ferrell (FF) superfluid without spin imbalance in a three-dimensional fermionic cold atom optical lattice, where s- and p-orbital bands of the lattice are coupled by another weak moving optical lattice. Such coupling leads to a spin-independent asymmetric Fermi surface, which, together with the s-wave scattering interaction between two spins, yields an FF type of superfluid pairing. Unlike traditional schemes, our proposal does not rely on the spin imbalance (or an equivalent Zeeman field) to induce the Fermi surface mismatch and provides a completely new route for realizing FF superfluids.
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Affiliation(s)
- Zhen Zheng
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
- Key Laboratory of Quantum Information, and Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Chunlei Qu
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Xubo Zou
- Key Laboratory of Quantum Information, and Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
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11
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Uehlinger T, Jotzu G, Messer M, Greif D, Hofstetter W, Bissbort U, Esslinger T. Artificial graphene with tunable interactions. PHYSICAL REVIEW LETTERS 2013; 111:185307. [PMID: 24237536 DOI: 10.1103/physrevlett.111.185307] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2013] [Revised: 10/11/2013] [Indexed: 06/02/2023]
Abstract
We create an artificial graphene system with tunable interactions and study the crossover from metallic to Mott insulating regimes, both in isolated and coupled two-dimensional honeycomb layers. The artificial graphene consists of a two-component spin mixture of an ultracold atomic Fermi gas loaded into a hexagonal optical lattice. For strong repulsive interactions, we observe a suppression of double occupancy and measure a gapped excitation spectrum. We present a quantitative comparison between our measurements and theory, making use of a novel numerical method to obtain Wannier functions for complex lattice structures. Extending our studies to time-resolved measurements, we investigate the equilibration of the double occupancy as a function of lattice loading time.
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Affiliation(s)
- Thomas Uehlinger
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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12
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Uchoa B, Barlas Y. Superconducting states in pseudo-Landau-levels of strained graphene. PHYSICAL REVIEW LETTERS 2013; 111:046604. [PMID: 23931391 DOI: 10.1103/physrevlett.111.046604] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2012] [Indexed: 06/02/2023]
Abstract
We describe the formation of superconducting states in graphene in the presence of pseudo-Landau-levels induced by strain, when time reversal symmetry is preserved. We show that superconductivity in strained graphene is quantum critical when the pseudo-Landau-levels are completely filled, whereas at partial fillings superconductivity survives at weak coupling. In the weak coupling limit, the critical temperature scales linearly with the coupling strength and shows a sequence of quantum critical points as a function of the filling factor that can be accessed experimentally. We argue that superconductivity can be induced by electron-phonon coupling and that the transition temperature can be controlled with the amount of strain and with the filling fraction of the Landau levels.
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Affiliation(s)
- Bruno Uchoa
- Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73069, USA
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13
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Yamamoto D, Sato C, Nikuni T, Tsuchiya S. Flow-induced charge modulation in superfluid atomic fermions loaded into an optical kagome lattice. PHYSICAL REVIEW LETTERS 2013; 110:145304. [PMID: 25167005 DOI: 10.1103/physrevlett.110.145304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2012] [Revised: 03/06/2013] [Indexed: 06/03/2023]
Abstract
We study the superfluid state of atomic fermions in a tunable optical kagome lattice motivated by recent experiments. We show that the imposed superflow induces spatial modulations in the density and order parameter of the pair condensate and leads to a charge modulated superfluid state analogous to a supersolid state. The spatial modulations in the superfluid emerge due to the geometric effect of the kagome lattice that introduces anisotropy in hopping amplitudes of fermion pairs in the presence of superflow. We also study superflow instabilities and find that the critical current limited by the dynamical instability is quite enhanced due to the large density of states associated with the flatband. The charge modulated superfluid state can sustain high temperatures close to the transition temperature that is also enhanced due to the flatband and is therefore realizable in experiments.
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Affiliation(s)
- Daisuke Yamamoto
- Condensed Matter Theory Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Chika Sato
- Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
| | - Tetsuro Nikuni
- Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
| | - Shunji Tsuchiya
- Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
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14
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Shen Z, Radzihovsky L, Gurarie V. Reentrant BCS-BEC crossover and a superfluid-insulator transition in optical lattices. PHYSICAL REVIEW LETTERS 2012; 109:245302. [PMID: 23368340 DOI: 10.1103/physrevlett.109.245302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2012] [Indexed: 06/01/2023]
Abstract
We study the thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for a more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the nonmonotonic dependence of the chemical potential on detuning and the concomitant Cooper-pair or molecular size, larger in the BCS and smaller in the BEC regimes. For a single filled band we find a quantum phase transition from a band insulator to a BCS-BEC superfluid, and map out the corresponding phase diagram.
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Affiliation(s)
- Zhaochuan Shen
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
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15
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Vishveshwara S. A glimpse of quantum phenomena in optical lattices. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:2916-2929. [PMID: 22615468 DOI: 10.1098/rsta.2011.0248] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Optical lattices in cold atomic systems offer an excellent setting for realizing quantum condensed matter phenomena. Here, a glimpse of such a setting is provided for the non-specialist. Some basic aspects of cold atomic gases and optical lattices are reviewed. Quantum many-body physics is explored in the case of interacting bosons on a lattice. Quantum behaviour in the presence of a potential landscape is examined for three different cases: a hexagonal lattice potential, a quasi-periodic potential and a disorder potential.
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Affiliation(s)
- Smitha Vishveshwara
- Department of Physics, Loomis Laboratories, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
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16
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Tarruell L, Greif D, Uehlinger T, Jotzu G, Esslinger T. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 2012; 483:302-5. [PMID: 22422263 DOI: 10.1038/nature10871] [Citation(s) in RCA: 712] [Impact Index Per Article: 59.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2011] [Accepted: 01/17/2012] [Indexed: 11/09/2022]
Abstract
Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other-a situation that has recently attracted considerable theoretical interest but that is extremely challenging to observe in solids. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.
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Affiliation(s)
- Leticia Tarruell
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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17
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Yu Y, Yang K. Simulating the Wess-Zumino supersymmetry model in optical lattices. PHYSICAL REVIEW LETTERS 2010; 105:150605. [PMID: 21230884 DOI: 10.1103/physrevlett.105.150605] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2010] [Revised: 09/11/2010] [Indexed: 05/30/2023]
Abstract
We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.
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Affiliation(s)
- Yue Yu
- Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
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18
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Herbut IF. Topological insulator in the core of the superconducting vortex in graphene. PHYSICAL REVIEW LETTERS 2010; 104:066404. [PMID: 20366839 DOI: 10.1103/physrevlett.104.066404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2009] [Indexed: 05/29/2023]
Abstract
The core of the vortex in a general superconducting order parameter in graphene is argued to be ordered, with the possible local order parameters forming the algebra U(1) x Cl(3). A sufficiently strong Zeeman coupling of the magnetic field of the vortex to the electron spin breaks the degeneracy in the core in favor of the anomalous quantum Hall state. I consider a variety of superconducting condensates on the honeycomb lattice and demonstrate the surprising universality of this result. A way to experimentally determine the outcome of the possible competition between different types of orders in the core is proposed.
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Affiliation(s)
- Igor F Herbut
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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19
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Kopnin NB, Sonin EB. BCS Superconductivity of Dirac electrons in graphene layers. PHYSICAL REVIEW LETTERS 2008; 100:246808. [PMID: 18643614 DOI: 10.1103/physrevlett.100.246808] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2008] [Indexed: 05/26/2023]
Abstract
Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point.
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Affiliation(s)
- N B Kopnin
- Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015 HUT, Finland
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Dietl P, Piéchon F, Montambaux G. New magnetic field dependence of Landau levels in a graphenelike structure. PHYSICAL REVIEW LETTERS 2008; 100:236405. [PMID: 18643528 DOI: 10.1103/physrevlett.100.236405] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2007] [Indexed: 05/26/2023]
Abstract
We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic in the other. We find that, in this case, the energy of the Landau levels varies with the field B as epsilon(n)(B) ~ [(n+gamma)B](2/3). This result is obtained from the low-field study of the tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter spectrum) as well as from a calculation in the continuum approximation at low field. The latter links the new spectrum to the one of a modified quartic oscillator. The obtained value gamma=1/2 is found to result from the cancellation of a Berry phase.
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Affiliation(s)
- Petra Dietl
- Laboratoire de Physique des Solides, Université Paris Sud, CNRS UMR8502, Orsay Cedex, France
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Zhu SL, Wang B, Duan LM. Simulation and detection of dirac fermions with cold atoms in an optical lattice. PHYSICAL REVIEW LETTERS 2007; 98:260402. [PMID: 17678070 DOI: 10.1103/physrevlett.98.260402] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2007] [Indexed: 05/16/2023]
Abstract
We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.
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Affiliation(s)
- Shi-Liang Zhu
- ICMP and LPIT, Department of Physics, South China Normal University, Guangzhou, China
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