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Diboraperylene Diborinic Acid Self-Assembly on Ag(111)-Kagome Flat Band Localized States Imaged by Scanning Tunneling Microscopy and Spectroscopy. Angew Chem Int Ed Engl 2024; 63:e202400313. [PMID: 38316614 DOI: 10.1002/anie.202400313] [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: 01/05/2024] [Revised: 02/02/2024] [Accepted: 02/05/2024] [Indexed: 02/07/2024]
Abstract
Replacement of sp2-hybridized carbon in polycyclic aromatic hydrocarbons (PAHs) by boron affords electron-deficient π-scaffolds due to the vacant pz-orbital of three-coordinate boron with the potential for pronounced electronic interactions with electron-rich metal surfaces. Using a diboraperylene diborinic acid derivative as precursor and a controlled on-surface non-covalent synthesis approach, we report on a self-assembled chiral supramolecular kagome network on an Ag(111) surface stabilized by intermolecular hydrogen-bonding interactions at low temperature. Scanning tunneling microscopy (STM) and spectroscopy (STS) reveal a flat band at ca. 0.33 eV above the Fermi level which is localized at the molecule center, in good agreement with tight-binding model calculations of flat bands characteristic for kagome lattices.
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2
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Electron Glass Phase with Resilient Zhang-Rice Singlets in LiCu_{3}O_{3}. PHYSICAL REVIEW LETTERS 2024; 132:126502. [PMID: 38579201 DOI: 10.1103/physrevlett.132.126502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Accepted: 02/12/2024] [Indexed: 04/07/2024]
Abstract
LiCu_{3}O_{3} is an antiferromagnetic mixed valence cuprate where trilayers of edge-sharing Cu(II)O (3d^{9}) are sandwiched in between planes of Cu(I) (3d^{10}) ions, with Li stochastically substituting Cu(II). Angle-resolved photoemission spectroscopy (ARPES) and density functional theory reveal two insulating electronic subsystems that are segregated in spite of sharing common oxygen atoms: a Cu d_{z^{2}}/O p_{z} derived valence band (VB) dispersing on the Cu(I) plane, and a Cu 3d_{x^{2}-y^{2}}/O 2p_{x,y} derived Zhang-Rice singlet (ZRS) band dispersing on the Cu(II)O planes. First-principle analysis shows the Li substitution to stabilize the insulating ground state, but only if antiferromagnetic correlations are present. Li further induces substitutional disorder and a 2D electron glass behavior in charge transport, reflected in a large 530 meV Coulomb gap and a linear suppression of VB spectral weight at E_{F} that is observed by ARPES. Surprisingly, the disorder leaves the Cu(II)-derived ZRS largely unaffected. This indicates a local segregation of Li and Cu atoms onto the two separate corner-sharing Cu(II)O_{2} sub-lattices of the edge-sharing Cu(II)O planes, and highlights the ubiquitous resilience of the entangled two hole ZRS entity against impurity scattering.
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3
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Parity-time-symmetric photonic topological insulator. NATURE MATERIALS 2024; 23:377-382. [PMID: 38195865 DOI: 10.1038/s41563-023-01773-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Accepted: 11/28/2023] [Indexed: 01/11/2024]
Abstract
Topological insulators are a concept that originally stems from condensed matter physics. As a corollary to their hallmark protected edge transport, the conventional understanding of such systems holds that they are intrinsically closed, that is, that they are assumed to be entirely isolated from the surrounding world. Here, by demonstrating a parity-time-symmetric topological insulator, we show that topological transport exists beyond these constraints. Implemented on a photonic platform, our non-Hermitian topological system harnesses the complex interplay between a discrete coupling protocol and judiciously placed losses and, as such, inherently constitutes an open system. Nevertheless, even though energy conservation is violated, our system exhibits an entirely real eigenvalue spectrum as well as chiral edge transport. Along these lines, this work enables the study of the dynamical properties of topological matter in open systems without the instability arising from complex spectra. Thus, it may inspire the development of compact active devices that harness topological features on-demand.
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4
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Observation of a Higher-Order End Topological Insulator in a Real Projective Lattice. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2024; 11:e2303222. [PMID: 38214384 PMCID: PMC10953588 DOI: 10.1002/advs.202303222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Revised: 08/15/2023] [Indexed: 01/13/2024]
Abstract
The modern theory of quantized polarization has recently extended from 1D dipole moment to multipole moment, leading to the development from conventional topological insulators (TIs) to higher-order TIs, i.e., from the bulk polarization as primary topological index, to the fractional corner charge as secondary topological index. The authors here extend this development by theoretically discovering a higher-order end TI (HOETI) in a real projective lattice and experimentally verifying the prediction using topolectric circuits. A HOETI realizes a dipole-symmetry-protected phase in a higher-dimensional space (conventionally in one dimension), which manifests as 0D topologically protected end states and a fractional end charge. The discovered bulk-end correspondence reveals that the fractional end charge, which is proportional to the bulk topological invariant, can serve as a generic bulk probe of higher-order topology. The authors identify the HOETI experimentally by the presence of localized end states and a fractional end charge. The results demonstrate the existence of fractional charges in non-Euclidean manifolds and open new avenues for understanding the interplay between topological obstructions in real and momentum space.
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Pseudo-fermion functional renormalization group for spin models. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:036501. [PMID: 38241725 DOI: 10.1088/1361-6633/ad208c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Accepted: 01/19/2024] [Indexed: 01/21/2024]
Abstract
For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow ofm-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.
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High Resolution Polar Kerr Effect Studies of CsV_{3}Sb_{5}: Tests for Time-Reversal Symmetry Breaking below the Charge-Order Transition. PHYSICAL REVIEW LETTERS 2023; 131:016901. [PMID: 37478434 DOI: 10.1103/physrevlett.131.016901] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Revised: 05/02/2023] [Accepted: 05/31/2023] [Indexed: 07/23/2023]
Abstract
We report high resolution polar Kerr effect measurements on CsV_{3}Sb_{5} single crystals in search of signatures of spontaneous time-reversal symmetry breaking below the charge-order transition at T^{*}≈94 K. Utilizing two different versions of zero-area loop Sagnac interferometers operating at 1550 nm wavelength, each with the fundamental attribute that without a time-reversal symmetry breaking sample at its path, the interferometer is perfectly reciprocal, we find no observable Kerr effect to within the noise floor limit of the apparatus at 30 nanoradians. Simultaneous coherent reflection ratio measurements confirm the sharpness of the charge-order transition in the same optical volume as the Kerr measurements. At finite magnetic field we observe a sharp onset of a diamagnetic shift in the Kerr signal at T^{*}, which persists down to the lowest temperature without change in trend. Since 1550 nm is an energy that was shown to capture all features of the optical properties of the material that interact with the charge-order transition, we are led to conclude that it is highly unlikely that time-reversal symmetry is broken in the charge ordered state in CsV_{3}Sb_{5}.
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7
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Hyperbolic Fringe Signal for Twin Impurity Quasiparticle Interference. PHYSICAL REVIEW LETTERS 2023; 130:256001. [PMID: 37418713 DOI: 10.1103/physrevlett.130.256001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Revised: 10/31/2022] [Accepted: 05/17/2023] [Indexed: 07/09/2023]
Abstract
We study the quasiparticle interference (QPI) pattern emanating from a pair of adjacent impurities on the surface of a gapped superconductor (SC). We find that hyperbolic fringes (HFs) in the QPI signal can appear due to the loop contribution of the two-impurity scattering, where the locations of the two impurities are the hyperbolic focus points. For a single pocket Fermiology, a HF pattern signals chiral SC order for nonmagnetic impurities and requires magnetic impurities for a nonchiral SC. For a multipocket scenario, a sign-changing order parameter such as an s_{±} wave likewise yields a HF signature. We discuss twin impurity QPI as a new tool to complement the analysis of superconducting order from local spectroscopy.
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8
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Interaction Effects in a 1D Flat Band at a Topological Crystalline Step Edge. NANO LETTERS 2023; 23:2476-2482. [PMID: 36972710 PMCID: PMC10103314 DOI: 10.1021/acs.nanolett.2c03794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 03/05/2023] [Indexed: 06/18/2023]
Abstract
Step edges of topological crystalline insulators can be viewed as predecessors of higher-order topology, as they embody one-dimensional edge channels embedded in an effective three-dimensional electronic vacuum emanating from the topological crystalline insulator. Using scanning tunneling microscopy and spectroscopy, we investigate the behavior of such edge channels in Pb1-xSnxSe under doping. Once the energy position of the step edge is brought close to the Fermi level, we observe the opening of a correlation gap. The experimental results are rationalized in terms of interaction effects which are enhanced since the electronic density is collapsed to a one-dimensional channel. This constitutes a unique system to study how topology and many-body electronic effects intertwine, which we model theoretically through a Hartree-Fock analysis.
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Hyperbolic matter in electrical circuits with tunable complex phases. Nat Commun 2023; 14:622. [PMID: 36739281 PMCID: PMC9899218 DOI: 10.1038/s41467-023-36359-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2022] [Accepted: 01/24/2023] [Indexed: 02/06/2023] Open
Abstract
Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states.
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10
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Hyperbolic Topological Band Insulators. PHYSICAL REVIEW LETTERS 2022; 129:246402. [PMID: 36563257 DOI: 10.1103/physrevlett.129.246402] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Revised: 10/13/2022] [Accepted: 10/26/2022] [Indexed: 06/17/2023]
Abstract
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-) dimensional momentum space. To explore the uncharted topological aspects arising in hyperbolic band theory, we here introduce elementary models of hyperbolic topological band insulators: the hyperbolic Haldane model and the hyperbolic Kane-Mele model; both obtained by replacing the hexagonal cells of their Euclidean counterparts by octagons. Their nontrivial topology is revealed by computing topological invariants in both position and momentum space. The bulk-boundary correspondence is evidenced by comparing bulk and boundary density of states, by modeling propagation of edge excitations, and by their robustness against disorder.
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11
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Experimental Identification of the Second-Order Non-Hermitian Skin Effect with Physics-Graph-Informed Machine Learning. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2022; 9:e2202922. [PMID: 36372546 PMCID: PMC9799024 DOI: 10.1002/advs.202202922] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Revised: 07/13/2022] [Indexed: 06/16/2023]
Abstract
Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems. The topological invariant of the bulk in d dimensions corresponds to the number of (d - 1)-dimensional boundary states. By extension, higher-order topological insulators reveal a bulk-edge-corner correspondence, such that nth order topological phases feature (d - n)-dimensional boundary states. The advent of non-Hermitian topological systems sheds new light on the emergence of the non-Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher-order NHSE remains largely unexplored, particularly in the experiment. An unsupervised approach-physics-graph-informed machine learning (PGIML)-to enhance the data mining ability of machine learning with limited domain knowledge is introduced. Through PGIML, the second-order NHSE in a 2D non-Hermitian topoelectrical circuit is experimentally demonstrated. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk-boundary correspondence in the second-order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non-Hermitian systems.
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12
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Discovery of conjoined charge density waves in the kagome superconductor CsV 3Sb 5. Nat Commun 2022; 13:6348. [PMID: 36289236 PMCID: PMC9606281 DOI: 10.1038/s41467-022-33995-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 10/07/2022] [Indexed: 11/09/2022] Open
Abstract
The electronic instabilities in CsV3Sb5 are believed to originate from the V 3d-electrons on the kagome plane, however the role of Sb 5p-electrons for 3-dimensional orders is largely unexplored. Here, using resonant tender X-ray scattering and high-pressure X-ray scattering, we report a rare realization of conjoined charge density waves (CDWs) in CsV3Sb5, where a 2 × 2 × 1 CDW in the kagome sublattice and a Sb 5p-electron assisted 2 × 2 × 2 CDW coexist. At ambient pressure, we discover a resonant enhancement on Sb L1-edge (2s→5p) at the 2 × 2 × 2 CDW wavevectors. The resonance, however, is absent at the 2 × 2 × 1 CDW wavevectors. Applying hydrostatic pressure, CDW transition temperatures are separated, where the 2 × 2 × 2 CDW emerges 4 K above the 2 × 2 × 1 CDW at 1 GPa. These observations demonstrate that symmetry-breaking phases in CsV3Sb5 go beyond the minimal framework of kagome electronic bands near van Hove filling.
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13
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Observation of room temperature excitons in an atomically thin topological insulator. Nat Commun 2022; 13:6313. [PMID: 36274087 PMCID: PMC9588767 DOI: 10.1038/s41467-022-33822-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2022] [Accepted: 10/04/2022] [Indexed: 11/23/2022] Open
Abstract
Optical spectroscopy of ultimately thin materials has significantly enhanced our understanding of collective excitations in low-dimensional semiconductors. This is particularly reflected by the rich physics of excitons in atomically thin crystals which uniquely arises from the interplay of strong Coulomb correlation, spin-orbit coupling (SOC), and lattice geometry. Here we extend the field by reporting the observation of room temperature excitons in a material of non-trivial global topology. We study the fundamental optical excitation spectrum of a single layer of bismuth atoms epitaxially grown on a SiC substrate (hereafter bismuthene or Bi/SiC) which has been established as a large-gap, two-dimensional (2D) quantum spin Hall (QSH) insulator. Strongly developed optical resonances are observed to emerge around the direct gap at the K and K’ points of the Brillouin zone, indicating the formation of bound excitons with considerable oscillator strength. These experimental findings are corroborated, concerning both the character of the excitonic resonances as well as their energy scale, by ab-initio GW and Bethe-Salpeter equation calculations, confirming strong Coulomb interaction effects in these optical excitations. Our observations provide evidence of excitons in a 2D QSH insulator at room temperature, with excitonic and topological physics deriving from the very same electronic structure. Here, the authors report the observation of room temperature excitons in a single layer of bismuth atoms epitaxially grown on a SiC substrate - a material of non-trivial global topology - with excitonic and topological physics deriving from the very same electronic structure.
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Abstract
The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter. Spaces with negative curvature are difficult to realise and investigate experimentally, but they can be emulated with synthetic matter. Here, the authors show how to do this using an electric circuit network, and present a method to characterize and verify the hyperbolic nature of the implemented model.
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15
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Universality of Hofstadter Butterflies on Hyperbolic Lattices. PHYSICAL REVIEW LETTERS 2022; 128:166402. [PMID: 35522481 DOI: 10.1103/physrevlett.128.166402] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 03/30/2022] [Indexed: 06/14/2023]
Abstract
Motivated by recent realizations of hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. Utilizing large hyperbolic lattices with periodic boundary conditions, we obtain the true bulk spectrum unaffected by boundary states. The butterfly spectrum with large extended gapped regions prevails, and its shape is universally determined by the fundamental tile, while the fractal structure is lost. We explain how these features originate from Landau levels in hyperbolic space and can be verified experimentally.
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Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate. PHYSICAL REVIEW LETTERS 2022; 128:167002. [PMID: 35522509 DOI: 10.1103/physrevlett.128.167002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 03/29/2022] [Indexed: 06/14/2023]
Abstract
Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the on-site term is paramount. Recently, the onset of superconductivity at 4.7 K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.
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Erratum: Analysis of Charge Order in the Kagome Metal AV_{3}Sb_{5} (A=K,Rb,Cs) [Phys. Rev. Lett. 127, 217601 (2021)]. PHYSICAL REVIEW LETTERS 2022; 128:099901. [PMID: 35302838 DOI: 10.1103/physrevlett.128.099901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Indexed: 06/14/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevLett.127.217601.
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High- T c superconductor Fe(Se,Te) monolayer: an intrinsic, scalable and electrically tunable Majorana platform. Natl Sci Rev 2022; 9:nwab087. [PMID: 35308561 PMCID: PMC8924703 DOI: 10.1093/nsr/nwab087] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Revised: 04/25/2021] [Accepted: 04/25/2021] [Indexed: 11/30/2022] Open
Abstract
Iron-based superconductors have been identified as a novel platform for realizing Majorana zero modes (MZMs) without heterostructures, due to their intrinsic topological properties and high-T c superconductivity. In the two-dimensional limit, the FeTe1-x Se x monolayer, a topological band inversion has recently been experimentally observed. Here, we propose to create MZMs by applying an in-plane magnetic field to the FeTe1-x Se x monolayer and tuning the local chemical potential via electric gating. Owing to the anisotropic magnetic couplings on edges, an in-plane magnetic field drives the system into an intrinsic high-order topological superconductor phase with Majorana corner modes. Furthermore, MZMs can occur at the domain wall of chemical potentials at either one edge or certain type of tri-junction in the two-dimensional bulk. Our study not only reveals the FeTe1-x Se x monolayer as a promising Majorana platform with scalability and electrical tunability and within reach of contemporary experimental capability, but also provides a general principle to search for realistic realization of high-order topological superconductivity.
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Analysis of Charge Order in the Kagome Metal AV_{3}Sb_{5} (A=K,Rb,Cs). PHYSICAL REVIEW LETTERS 2021; 127:217601. [PMID: 34860107 DOI: 10.1103/physrevlett.127.217601] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 10/20/2021] [Indexed: 05/16/2023]
Abstract
Motivated by the recent discovery of unconventional charge order, we develop a theory of electronically mediated charge density wave formation in the family of kagome metals AV_{3}Sb_{5} (A=K,Rb,Cs). The intertwining of van Hove filling and sublattice interference suggests a three-fold charge density wave instability at T_{CDW}. From there, the charge order forming below T_{CDW} can unfold into a variety of phases capable of exhibiting orbital currents and nematicity. We develop a Ginzburg Landau formalism to stake out the parameter space of kagome charge order. We find a nematic chiral charge order to be energetically preferred, which shows tentative agreement with experimental evidence.
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Nature of Unconventional Pairing in the Kagome Superconductors AV_{3}Sb_{5} (A=K,Rb,Cs). PHYSICAL REVIEW LETTERS 2021; 127:177001. [PMID: 34739258 DOI: 10.1103/physrevlett.127.177001] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Revised: 07/29/2021] [Accepted: 09/02/2021] [Indexed: 05/12/2023]
Abstract
The recent discovery of AV_{3}Sb_{5} (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for AV_{3}Sb_{5}, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in AV_{3}Sb_{5}.
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21
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Unconventional chiral charge order in kagome superconductor KV 3Sb 5. NATURE MATERIALS 2021; 20:1353-1357. [PMID: 34112979 DOI: 10.1038/s41563-021-01034-y] [Citation(s) in RCA: 121] [Impact Index Per Article: 40.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2021] [Accepted: 05/06/2021] [Indexed: 06/12/2023]
Abstract
Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1-4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.
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Abstract
We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.
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Abstract
Interacting bosonic particles in artificial lattices have proven to be a powerful tool for the investigation of exotic phases of matter as well as phenomena resulting from nontrivial topology. Exciton-polaritons, bosonic quasi-particles of light and matter, have been shown to combine the on-chip benefits of optical systems with strong interactions, inherited from their matter character. Technologically significant semiconductor platforms strictly require cryogenic temperatures. In this communication, we demonstrate exciton-polariton lasing for topological defects emerging from the imprinted lattice structure at room temperature. We utilize red fluorescent protein derived from DsRed of Discosoma sea anemones, hosting highly stable Frenkel excitons. Using a patterned mirror cavity, we tune the lattice potential landscape of a linear Su-Schrieffer-Heeger chain to design topological defects at domain boundaries and at the edge. We unequivocally demonstrate polariton lasing from these topological defects. This progress has paved the road to interacting boson many-body physics under ambient conditions.
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Abstract
The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally different approaches to protected information transmission and wave guidance. A particularly promising emergent technology is based on recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations, and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.
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Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs. Nat Commun 2021; 12:3650. [PMID: 34131129 PMCID: PMC8206138 DOI: 10.1038/s41467-021-23727-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 05/12/2021] [Indexed: 11/16/2022] Open
Abstract
Since the early days of Dirac flux quantization, magnetic monopoles have been sought after as a potential corollary of quantized electric charge. As opposed to magnetic monopoles embedded into the theory of electromagnetism, Weyl semimetals (WSM) exhibit Berry flux monopoles in reciprocal parameter space. As a function of crystal momentum, such monopoles locate at the crossing point of spin-polarized bands forming the Weyl cone. Here, we report momentum-resolved spectroscopic signatures of Berry flux monopoles in TaAs as a paradigmatic WSM. We carried out angle-resolved photoelectron spectroscopy at bulk-sensitive soft X-ray energies (SX-ARPES) combined with photoelectron spin detection and circular dichroism. The experiments reveal large spin- and orbital-angular-momentum (SAM and OAM) polarizations of the Weyl-fermion states, resulting from the broken crystalline inversion symmetry in TaAs. Supported by first-principles calculations, our measurements image signatures of a topologically non-trivial winding of the OAM at the Weyl nodes and unveil a chirality-dependent SAM of the Weyl bands. Our results provide directly bulk-sensitive spectroscopic support for the non-trivial band topology in the WSM TaAs, promising to have profound implications for the study of quantum-geometric effects in solids. Weyl semimetals exhibit Berry flux monopoles in momentum-space, but direct experimental evidence has remained elusive. Here, the authors reveal topologically non-trivial winding of the orbital-angular-momentum at the Weyl nodes and a chirality-dependent spin-angular-momentum of the Weyl bands, as a direct signature of the Berry flux monopoles in TaAs.
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Topological Defect Engineering and PT Symmetry in Non-Hermitian Electrical Circuits. PHYSICAL REVIEW LETTERS 2021; 126:215302. [PMID: 34114871 DOI: 10.1103/physrevlett.126.215302] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 04/21/2021] [Indexed: 06/12/2023]
Abstract
We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry PT and chiral symmetry anti-PT (APT). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of PT-symmetric gain and loss on localized edge and defect states in a non-Hermitian Su-Schrieffer-Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the APT-symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel PT-symmetric Z_{2} invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not PT symmetric, the topological defect state disappears and only reemerges when APT symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.
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Abstract
A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in Scandium Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction, is enhanced by a factor of about 3.2 as compared to graphene. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put the turbulent flow regime described by holography within the reach of experiments.
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Evidence for a three-dimensional quantum spin liquid in PbCuTe 2O 6. Nat Commun 2020; 11:2348. [PMID: 32393775 PMCID: PMC7214440 DOI: 10.1038/s41467-020-15594-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Accepted: 02/29/2020] [Indexed: 11/12/2022] Open
Abstract
The quantum spin liquid is a highly entangled magnetic state characterized by the absence of static magnetism in its ground state. Instead, the spins fluctuate in a highly correlated way down to the lowest temperatures. Quantum spin liquids are very rare and are confined to a few specific cases where the interactions between the magnetic ions cannot be simultaneously satisfied (known as frustration). Lattices with magnetic ions in triangular or tetrahedral arrangements, which interact via isotropic antiferromagnetic interactions, can generate such a frustration. Three-dimensional isotropic spin liquids have mostly been sought in materials where the magnetic ions form pyrochlore or hyperkagome lattices. Here we present a three-dimensional lattice called the hyper-hyperkagome that enables spin liquid behaviour and manifests in the compound PbCuTe2O6. Using a combination of experiment and theory, we show that this system exhibits signs of being a quantum spin liquid with no detectable static magnetism together with the presence of diffuse continua in the magnetic spectrum suggestive of fractional spinon excitations. Quantum spin liquids have magnetic moments that do not form magnetic order even as the temperature approaches zero, leading to the dominance of quantum fluctuations. Chillal et al. present evidence that the hyper-hyperkagome lattice of PbCuTe2O6 hosts a three-dimensional quantum spin liquid.
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Abstract
Dissipation is a general feature of non-Hermitian systems. But rather than being an unavoidable nuisance, non-Hermiticity can be precisely controlled and hence used for sophisticated applications, such as optical sensors with enhanced sensitivity. In our work, we implement a non-Hermitian photonic mesh lattice by tailoring the anisotropy of the nearest-neighbor coupling. The appearance of an interface results in a complete collapse of the entire eigenmode spectrum, leading to an exponential localization of all modes at the interface. As a consequence, any light field within the lattice travels toward this interface, irrespective of its shape and input position. On the basis of this topological phenomenon, called the "non-Hermitian skin effect," we demonstrate a highly efficient funnel for light.
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Chiral Voltage Propagation and Calibration in a Topolectrical Chern Circuit. PHYSICAL REVIEW LETTERS 2019; 122:247702. [PMID: 31322409 DOI: 10.1103/physrevlett.122.247702] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2018] [Indexed: 06/10/2023]
Abstract
We propose an electric circuit array with topologically protected unidirectional voltage modes at its boundary. Instead of external bias fields or Floquet engineering, we employ negative impedance converters with current inversion (INICs) to accomplish a nonreciprocal, time-reversal symmetry-broken electronic network we call a topolectrical Chern circuit (TCC). The TCC features an admittance bulk gap fully tunable via the resistors used in the INICs, along with a chiral voltage boundary mode reminiscent of the Berry flux monopole present in the admittance band structure. The active circuit elements in the TCC can be calibrated to compensate for dissipative loss.
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31
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Orbital Fingerprint of Topological Fermi Arcs in the Weyl Semimetal TaP. PHYSICAL REVIEW LETTERS 2019; 122:116402. [PMID: 30951331 DOI: 10.1103/physrevlett.122.116402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Revised: 11/19/2018] [Indexed: 06/09/2023]
Abstract
The monopnictides TaAs and TaP are well-established Weyl semimetals. Yet, a precise assignment of Fermi arcs, accommodating the predicted chiral charge of the bulk Weyl points, has been difficult in these systems, and the topological character of different surface features in the Fermi surface is not fully understood. Here, employing a joint analysis from linear dichroism in angle-resolved photoemission and first-principles calculations, we unveil the orbital texture on the full Fermi surface of TaP(001). We observe pronounced switches in the orbital texture at the projected Weyl nodes, and show how they facilitate a topological classification of the surface band structure. Our findings establish a critical role of the orbital degrees of freedom in mediating the surface-bulk connectivity in Weyl semimetals.
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Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1 T-TaSe 2 mediated by mode-selective electron-phonon coupling. SCIENCE ADVANCES 2019; 5:eaav4449. [PMID: 30838333 PMCID: PMC6397029 DOI: 10.1126/sciadv.aav4449] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Accepted: 01/14/2019] [Indexed: 06/09/2023]
Abstract
Quantum materials represent one of the most promising frontiers in the quest for faster, lightweight, energy-efficient technologies. However, their inherent complexity and rich phase landscape make them challenging to understand or manipulate. Here, we present a new ultrafast electron calorimetry technique that can systematically uncover new phases of quantum matter. Using time- and angle-resolved photoemission spectroscopy, we measure the dynamic electron temperature, band structure, and heat capacity. This approach allows us to uncover a new long-lived metastable state in the charge density wave material 1T-TaSe2, which is distinct from all the known equilibrium phases: It is characterized by a substantially reduced effective total heat capacity that is only 30% of the normal value, because of selective electron-phonon coupling to a subset of phonon modes. As a result, less energy is required to melt the charge order and transform the state of the material than under thermal equilibrium conditions.
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Demonstration of a two-dimensional [Formula: see text]-symmetric crystal. Nat Commun 2019; 10:435. [PMID: 30683867 PMCID: PMC6347626 DOI: 10.1038/s41467-018-08104-x] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2018] [Accepted: 12/07/2018] [Indexed: 11/16/2022] Open
Abstract
With the discovery of [Formula: see text]-symmetric quantum mechanics, it was shown that even non-Hermitian systems may exhibit entirely real eigenvalue spectra. This finding did not only change the perception of quantum mechanics itself, it also significantly influenced the field of photonics. By appropriately designing one-dimensional distributions of gain and loss, it was possible to experimentally verify some of the hallmark features of [Formula: see text]-symmetry using electromagnetic waves. Nevertheless, an experimental platform to study the impact of [Formula: see text] -symmetry in two spatial dimensions has so far remained elusive. We break new grounds by devising a two-dimensional [Formula: see text]-symmetric system based on photonic waveguide lattices with judiciously designed refractive index landscape and alternating loss. With this system at hand, we demonstrate a non-Hermitian two-dimensional topological phase transition that is closely linked to the emergence of topological mid-gap edge states.
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Platform for Electrically Pumped Polariton Simulators and Topological Lasers. PHYSICAL REVIEW LETTERS 2018; 121:257402. [PMID: 30608796 DOI: 10.1103/physrevlett.121.257402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Indexed: 06/09/2023]
Abstract
Two-dimensional electronic materials such as graphene and transition metal dichalgenides feature unique electrical and optical properties due to the conspirative effect of band structure, orbital coupling, and crystal symmetry. Synthetic matter, as accomplished by artificial lattice arrangements of cold atoms, molecules, electron patterning, and optical cavities, has emerged to provide manifold intriguing frameworks to likewise realize such scenarios. Exciton polaritons have recently been added to the list of promising candidates for the emulation of system Hamiltonians on a semiconductor platform, offering versatile tools to engineer the potential landscape and to access the nonlinear electro-optical regime. In this work, we introduce an electronically driven square and honeycomb lattice of exciton polaritons, paving the way towards real world devices based on polariton lattices for on-chip applications. Our platform exhibits laserlike emission from high-symmetry points under direct current injection, hinting at the prospect of electrically driven polariton lasers with possibly topologically nontrivial properties.
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Three-Dimensional Electronic Structure of the Type-II Weyl Semimetal WTe_{2}. PHYSICAL REVIEW LETTERS 2017; 119:026403. [PMID: 28753342 DOI: 10.1103/physrevlett.119.026403] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2017] [Indexed: 06/07/2023]
Abstract
By combining bulk sensitive soft-x-ray angular-resolved photoemission spectroscopy and first-principles calculations we explored the bulk electron states of WTe_{2}, a candidate type-II Weyl semimetal featuring a large nonsaturating magnetoresistance. Despite the layered geometry suggesting a two-dimensional electronic structure, we directly observe a three-dimensional electronic dispersion. We report a band dispersion in the reciprocal direction perpendicular to the layers, implying that electrons can also travel coherently when crossing from one layer to the other. The measured Fermi surface is characterized by two well-separated electron and hole pockets at either side of the Γ point, differently from previous more surface sensitive angle-resolved photoemission spectroscopy experiments that additionally found a pronounced quasiparticle weight at the zone center. Moreover, we observe a significant sensitivity of the bulk electronic structure of WTe_{2} around the Fermi level to electronic correlations and renormalizations due to self-energy effects, previously neglected in first-principles descriptions.
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Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material. Science 2017; 357:287-290. [PMID: 28663438 DOI: 10.1126/science.aai8142] [Citation(s) in RCA: 278] [Impact Index Per Article: 39.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2016] [Revised: 12/16/2016] [Accepted: 06/09/2017] [Indexed: 11/02/2022]
Abstract
Quantum spin Hall materials hold the promise of revolutionary devices with dissipationless spin currents but have required cryogenic temperatures owing to small energy gaps. Here we show theoretically that a room-temperature regime with a large energy gap may be achievable within a paradigm that exploits the atomic spin-orbit coupling. The concept is based on a substrate-supported monolayer of a high-atomic number element and is experimentally realized as a bismuth honeycomb lattice on top of the insulating silicon carbide substrate SiC(0001). Using scanning tunneling spectroscopy, we detect a gap of ~0.8 electron volt and conductive edge states consistent with theory. Our combined theoretical and experimental results demonstrate a concept for a quantum spin Hall wide-gap scenario, where the chemical potential resides in the global system gap, ensuring robust edge conductance.
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Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics. PHYSICAL REVIEW LETTERS 2017; 118:246801. [PMID: 28665643 DOI: 10.1103/physrevlett.118.246801] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2016] [Indexed: 06/07/2023]
Abstract
We report on the scaling behavior of V-doped (Bi,Sb)_{2}Te_{3} samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of 1/2e^{2}/h in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from 1/2e^{2}/h Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of the signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.
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38
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Incommensurate quantum-size oscillations in acene-based molecular wires—Effects of quantum fluctuations. J Chem Phys 2017. [DOI: 10.1063/1.4975319] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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39
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Robust spin-polarized midgap states at step edges of topological crystalline insulators. Science 2016; 354:1269-1273. [DOI: 10.1126/science.aah6233] [Citation(s) in RCA: 76] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2016] [Accepted: 11/11/2016] [Indexed: 11/02/2022]
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Interacting Surface States of Three-Dimensional Topological Insulators. PHYSICAL REVIEW LETTERS 2015; 115:017001. [PMID: 26182115 DOI: 10.1103/physrevlett.115.017001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2014] [Indexed: 06/04/2023]
Abstract
We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite sign for electrons with opposite spin. Assuming density-density contact interactions, we find superconducting and anomalous (quantum) Hall phases for attractive and repulsive interactions, respectively, as well as chiral fermion and chiral Majorana fermion boundary modes between different phases. Our setup is preeminently adapted to the search for topologically ordered surface terminations that could be microscopically stabilized by tailored surface interaction profiles.
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Topological nature and the multiple Dirac cones hidden in Bismuth high-Tc superconductors. Sci Rep 2015; 5:10435. [PMID: 26014056 PMCID: PMC4444835 DOI: 10.1038/srep10435] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2014] [Accepted: 04/13/2015] [Indexed: 12/01/2022] Open
Abstract
Recent theoretical studies employing density-functional theory have predicted BaBiO3 (when doped with electrons) and YBiO3 to become a topological insulator (TI) with a large topological gap (~0.7 eV). This, together with the natural stability against surface oxidation, makes the Bismuth-Oxide family of special interest for possible applications in quantum information and spintronics. The central question, we study here, is whether the hole-doped Bismuth Oxides, i.e. Ba1-xKxBiO3 and BaPb1-xBixO3, which are “high-Tc” bulk superconducting near 30 K, additionally display in the further vicinity of their Fermi energy EF a topological gap with a Dirac-type of topological surface state. Our electronic structure calculations predict the K-doped family to emerge as a TI, with a topological gap above EF. Thus, these compounds can become superconductors with hole-doping and potential TIs with additional electron doping. Furthermore, we predict the Bismuth-Oxide family to contain an additional Dirac cone below EF for further hole doping, which manifests these systems to be candidates for both electron- and hole-doped topological insulators.
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Quantum Paramagnet in a π Flux Triangular Lattice Hubbard Model. PHYSICAL REVIEW LETTERS 2015; 114:167201. [PMID: 25955072 DOI: 10.1103/physrevlett.114.167201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Indexed: 06/04/2023]
Abstract
We propose the π flux triangular lattice Hubbard model (π THM) as a prototypical setup to stabilize magnetically disordered quantum states of matter in the presence of charge fluctuations. The quantum paramagnetic domain of the π THM that we identify for intermediate Hubbard U is framed by a Dirac semimetal for weak coupling and by 120° Néel order for strong coupling. Generalizing the Klein duality from spin Hamiltonians to tight-binding models, the π THM maps to a Hubbard model which corresponds to the (J_{H},J_{K})=(-1,2) Heisenberg-Kitaev model in its strong coupling limit. The π THM provides a promising microscopic testing ground for exotic finite-U spin liquid ground states amenable to numerical investigation.
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Generalized Kitaev models and extrinsic non-Abelian twist defects. PHYSICAL REVIEW LETTERS 2015; 114:026401. [PMID: 25635553 DOI: 10.1103/physrevlett.114.026401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2014] [Indexed: 06/04/2023]
Abstract
We present a wide class of partially integrable lattice models with two-spin interactions which generalize the Kitaev honeycomb model. These models have a conserved quantity associated with each plaquette, conserved large loop operators on the torus, and topological degeneracy. We introduce a "slave-genon" approach which generalizes the Majorana fermion approach in the Kitaev model. The Hilbert space of our spin model can be embedded in an enlarged Hilbert space of non-Abelian twist defects, referred to as genons. In the enlarged Hilbert space, the spin model is exactly reformulated as a model of non-Abelian genons coupled to a discrete gauge field. We discuss in detail a particular Z_{3} generalization, and we show that in a certain limit the model is analytically tractable and produces a non-Abelian topological phase with chiral parafermion edge states.
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Momentum-space entanglement spectrum of bosons and fermions with interactions. PHYSICAL REVIEW LETTERS 2014; 113:256404. [PMID: 25554899 DOI: 10.1103/physrevlett.113.256404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2014] [Indexed: 06/04/2023]
Abstract
We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in Thomale et al. [Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may support the numerical study of phase transitions in the momentum space density matrix renormalization group.
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Theoretical prediction of a strongly correlated Dirac metal. Nat Commun 2014; 5:4261. [PMID: 24980208 DOI: 10.1038/ncomms5261] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Accepted: 05/30/2014] [Indexed: 11/09/2022] Open
Abstract
Recently, the most intensely studied objects in the electronic theory of solids have been strongly correlated systems and graphene. However, the fact that the Dirac bands in graphene are made up of sp(2) electrons, which are subject to neither strong Hubbard repulsion U nor strong Hund's rule coupling J, creates certain limitations in terms of novel, interaction-induced physics that could be derived from Dirac points. Here we propose GaCu3(OH)6Cl2 (Ga-substituted herbertsmithite) as a correlated Dirac-Kagome metal combining Dirac electrons, strong interactions and frustrated magnetic interactions. Using density functional theory, we calculate its crystallographic and electronic properties, and observe that it has symmetry-protected Dirac points at the Fermi level. Its many-body physics is diverse, with possible charge, magnetic and superconducting instabilities. Through a combination of various many-body methods we study possible symmetry-lowering phase transitions such as Mott-Hubbard, charge or magnetic ordering, and unconventional superconductivity, which in this compound assumes an f-wave symmetry.
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Model evidence of an anisotropic chiral d+id-wave pairing state for the water-intercalated Na(x)CoO2·yH2O superconductor. PHYSICAL REVIEW LETTERS 2013; 111:097001. [PMID: 24033062 DOI: 10.1103/physrevlett.111.097001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2013] [Revised: 06/12/2013] [Indexed: 06/02/2023]
Abstract
Since its discovery, the superconducting phase in water-intercalated sodium cobaltates Na(x)CoO2·yH2O (x∼0.3, y∼1.3) has posed fundamental challenges in terms of experimental investigation and theoretical understanding. By a combined cluster calculation and renormalization group approach, we find an anisotropic chiral d+id-wave state as a consequence of multiorbital effects, Fermi surface topology, and magnetic fluctuations. It naturally explains the singlet property and close-to-nodal gap features of the superconducting phase as indicated by experiments.
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Unconventional fermi surface instabilities in the kagome Hubbard model. PHYSICAL REVIEW LETTERS 2013; 110:126405. [PMID: 25166827 DOI: 10.1103/physrevlett.110.126405] [Citation(s) in RCA: 63] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2012] [Indexed: 05/12/2023]
Abstract
We investigate the competing Fermi surface instabilities in the kagome tight-binding model. Specifically, we consider on-site and short-range Hubbard interactions in the vicinity of van Hove filling of the dispersive kagome bands where the fermiology promotes the joint effect of enlarged density of states and nesting. The sublattice interference mechanism devised by Kiesel and Thomale [Phys. Rev. B 86, 121105 (2012)] allows us to explain the intricate interplay between ferromagnetic fluctuations and other ordering tendencies. On the basis of the functional renormalization group used to obtain an adequate low-energy theory description, we discover finite angular momentum spin and charge density wave order, a twofold degenerate d-wave Pomeranchuk instability, and f-wave superconductivity away from van Hove filling. Together, this makes the kagome Hubbard model the prototypical scenario for several unconventional Fermi surface instabilities.
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Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3. PHYSICAL REVIEW LETTERS 2012; 108:127203. [PMID: 22540620 DOI: 10.1103/physrevlett.108.127203] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2011] [Revised: 07/19/2011] [Indexed: 05/31/2023]
Abstract
Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2IrO3 (A=Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from θ≈-125 K for Na2IrO3 to θ≈-33 K for Li2IrO3, while the ordering temperature remains roughly the same T(N)≈15 K. Using functional renormalization group calculations we show that this evolution of θ and T(N) as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2IrO3 is deep in a magnetically ordered regime, while Li2IrO3 appears to be close to a spin-liquid regime.
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Tunable electron interactions and fractional quantum Hall States in graphene. PHYSICAL REVIEW LETTERS 2011; 107:176602. [PMID: 22107550 DOI: 10.1103/physrevlett.107.176602] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2011] [Indexed: 05/31/2023]
Abstract
The recent discovery of fractional quantum Hall (FQH) states in graphene raises the question of whether the physics of graphene offers any advantages over GaAs-based materials in exploring strongly correlated states of two-dimensional electrons. Here we propose a method to continuously tune the effective electron interactions in graphene and its bilayer by the dielectric environment of the sample. Using this method, the charge gaps of prominent FQH states, including ν=1/3 or ν=5/2 states, can be increased several times, or reduced to zero. The tunability of the interactions can be used to realize and stabilize various strongly correlated phases and explore the transitions between them.
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Exotic d-wave superconducting state of strongly hole-doped K(x)Ba(1-x)Fe2As2. PHYSICAL REVIEW LETTERS 2011; 107:117001. [PMID: 22026695 DOI: 10.1103/physrevlett.107.117001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2011] [Indexed: 05/31/2023]
Abstract
We investigate the superconducting phase in the K(x)Ba(1-x)Fe2As2 122 compounds from moderate to strong hole-doping regimes. Using the functional renormalization group, we show that, while the system develops a nodeless anisotropic s(±) order parameter in the moderately doped regime, gapping out the electron pockets at strong hole doping drives the system into a nodal (cos k(x) + cos k(y))(cos k(x) - cos k(y)) d-wave superconducting state. This is in accordance with recent experimental evidence from measurements on KFe2As2 which observe a nodal order parameter in the extreme doping regime. The magnetic instability is strongly suppressed.
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