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Mandal I, Freire H. Transport properties in non-Fermi liquid phases of nodal-point semimetals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:443002. [PMID: 39038487 DOI: 10.1088/1361-648x/ad665e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2024] [Accepted: 07/22/2024] [Indexed: 07/24/2024]
Abstract
In this review, we survey the current progress in computing transport properties in semimetals which harbour non-Fermi liquid (NFL) phases. We first discuss the widely-used Kubo formalism, which can be applied to the effective theory describing the stable NFL phase obtained via a renormalization group procedure and, hence, is applicable for temperatures close to zero (e.g. optical conductivity). For finite-temperature regimes, which apply to the computations of the generalized DC conductivity tensors, we elucidate the memory matrix approach. This approach is based on an effective hydrodynamic description of the system, and is especially suited for tackling transport calculations in strongly-interacting quantum field theories, because it does not rely on the existence of long-lived quasiparticles. As a concrete example, we apply these two approaches to find the response of the so-calledLuttinger-Abrikosov-Benelavskii phaseof isotropic three-dimensional Luttinger semimetals, which arises under the effects of long-ranged (unscreened) Coulomb interactions, with the chemical potential fine-tuned to cut exactly the nodal point. In particular, we focus on the electric conductivity tensors, thermal and thermoelectric response, Raman response, free energy, entropy density, and shear viscosity.
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Affiliation(s)
- Ipsita Mandal
- Department of Physics, Shiv Nadar Institution of Eminence (SNIoE), Gautam Buddha Nagar, Uttar Pradesh 201314, India
- Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, D-79104 Freiburg, Germany
| | - Hermann Freire
- Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia, GO, Brazil
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2
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Tang F, Chen Y, Ge XL, Meng WZ, Han ZD, Qian B, Zhao W, Jiang XF, Fang Y, Ju S. Anisotropic magnetoresistance and electronic features of the candidate topological compound praseodymium monobismuthide. Phys Chem Chem Phys 2023; 25:25573-25580. [PMID: 37721039 DOI: 10.1039/d3cp03480a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/19/2023]
Abstract
PrBi, a sister member of the rare-earth monopnictide family, is an excellent candidate for studying extreme magnetoresistance and nontrivial topological electronic states. In this study, we perform angular magnetoresistance measurements as well as bulk and surface band structure calculations on this compound. PrBi's magnetoresistance is revealed to be significantly angle-dependent and shows a fourfold symmetry as always observed in the nonmagnetic isostructural counterparts, including LaSb, LaBi, and LuBi. Its angular magnetoresistance can be reproduced well using the semiclassical two-band model. The deduced parameters suggest that PrBi hosts an elongated electron pocket with a mobility anisotropy of ∼3.13 and is slightly uncompensated in its carrier concentration. Our bulk and surface band structure calculations confirm the anisotropic electronic features. Moreover, we reveal that a nodal-line-shaped surface state appears at the X̄ point, and is associated with the quadratic dispersion along the -X̄ direction, and the linear type-I Dirac dispersion along the X̄-M̄ direction. Owing to the type-I Dirac dispersion feature, PrBi could serve as a promising material platform for studying many unexpected physical properties, such as the highly anisotropic transport and valley polarization of electrons.
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Affiliation(s)
- F Tang
- Jiangsu Key Laboratory of Thin Films, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
- Jiangsu Laboratory of Advanced Functional Materials, School of Electronic and Information Engineering, Changshu Institute of Technology, Changshu 215500, China.
| | - Y Chen
- Jiangsu Key Laboratory of Thin Films, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
- Jiangsu Laboratory of Advanced Functional Materials, School of Electronic and Information Engineering, Changshu Institute of Technology, Changshu 215500, China.
| | - X-L Ge
- Jiangsu Laboratory of Advanced Functional Materials, School of Electronic and Information Engineering, Changshu Institute of Technology, Changshu 215500, China.
| | - W-Z Meng
- School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Z-D Han
- Jiangsu Laboratory of Advanced Functional Materials, School of Electronic and Information Engineering, Changshu Institute of Technology, Changshu 215500, China.
| | - B Qian
- Jiangsu Laboratory of Advanced Functional Materials, School of Electronic and Information Engineering, Changshu Institute of Technology, Changshu 215500, China.
| | - W Zhao
- Department of Materials Science and Engineering, Monash University, Clayton, VIC 3800, Australia
| | - X-F Jiang
- Jiangsu Laboratory of Advanced Functional Materials, School of Electronic and Information Engineering, Changshu Institute of Technology, Changshu 215500, China.
| | - Y Fang
- Jiangsu Laboratory of Advanced Functional Materials, School of Electronic and Information Engineering, Changshu Institute of Technology, Changshu 215500, China.
| | - S Ju
- Jiangsu Key Laboratory of Thin Films, School of Physical Science and Technology, Soochow University, Suzhou 215006, China.
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Zhao PL, Qiang XB, Lu HZ, Xie XC. Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator. PHYSICAL REVIEW LETTERS 2021; 127:176601. [PMID: 34739297 DOI: 10.1103/physrevlett.127.176601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 09/16/2021] [Indexed: 06/13/2023]
Abstract
Topological insulators (TIs) are an exciting discovery because of their robustness against disorder and interactions. Recently, second-order TIs have been attracting increasing attention, because they host topologically protected 1D hinge states in 3D or 0D corner states in 2D. A significantly critical issue is whether the second-order TIs also survive interactions, but it is still unexplored. We study the effects of weak Coulomb interactions on a 3D second-order TI, with the help of renormalization-group calculations. We find that the 3D second-order TIs are always unstable, suffering from two types of topological phase transitions. One is from second-order TI to TI, the other is to normal insulator. The first type is accompanied by emergent time-reversal and inversion symmetries and has a dynamical critical exponent κ=1. The second type does not have the emergent symmetries but has nonuniversal dynamical critical exponents κ<1. Our results may inspire more inspections on the stability of higher-order topological states of matter and related novel quantum criticalities.
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Affiliation(s)
- Peng-Lu Zhao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Xiao-Bin Qiang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, West Building 3, No. 10, Xibeiwang East Road, Haidian District, Beijing 100193, China
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4
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Behera SK, Ahalawat M, Jana S, Samal P, Deb P. Renormalization group analysis of weakly interacting van der Waals Fermi system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:335604. [PMID: 34116520 DOI: 10.1088/1361-648x/ac0ab3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 06/11/2021] [Indexed: 06/12/2023]
Abstract
Weak-coupling phenomena of the two-dimensional Hubbard model is gaining momentum as a new interesting research field due to its extraordinarily rich behavior as a function of the carrier density and model parameters. Salmhofer (1998Commun.Math.Phys.194249; 2001Phys.Rev.Lett.87187004) developed a new renormalization-group method for interacting Fermi systems and Metzner (2000Phys.Rev. B617364; 2000Phys.Rev.Lett.855162) implemented this renormalization group analysis of the two-dimensional Hubbard model. In this work, we demonstrate the spin-wave dependent electronic structure and susceptibility behavior of model graphene-phosphorene van der Waals heterostructure in the framework of renormalization group approach. We implement singlet vertex response function for the weakly interacting van der Waals Fermi system with nearest-neighbor hopping amplitudes. This analytical approach is further extended for spin-wave dependent susceptibility behavior. We present the resulting compressibility and phase diagram in the vicinity of half-filling, and also results for the density dependence of the critical energy scale.
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Affiliation(s)
- Sushant Kumar Behera
- Density Functional Theory and Quantum Simulations Group (DFTQSG), School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Madhavi Ahalawat
- Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, India
| | - Subrata Jana
- Density Functional Theory and Quantum Simulations Group (DFTQSG), School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Prasanjit Samal
- Density Functional Theory and Quantum Simulations Group (DFTQSG), School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Pritam Deb
- Advanced Functional Material Laboratory (AFML), Department of Physics, Tezpur University (Central University), Tezpur, Assam 784028, India
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5
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Wang JR, Li W, Wang G, Zhang CJ. Global phase diagram of Coulomb-interacting anisotropic Weyl semimetal with disorder. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:125601. [PMID: 33326939 DOI: 10.1088/1361-648x/abd426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
Taking into account the interplay between the disorder and Coulomb interaction, the phase diagram of three-dimensional anisotropic Weyl semimetal is studied by renormalization group (RG) theory. Weak disorder is irrelevant in anisotropic Weyl semimetal, while the disorder becomes relevant and drives a quantum phase transition (QPT) from semimetal to compressible diffusive metal (CDM) phases if the disorder strength is larger than a critical value. The long-range Coulomb interaction is irrelevant in clean anisotropic Weyl semimetal. However, interestingly, we find that the long-range Coulomb interaction exerts a dramatic influence on the critical disorder strength for phase transition to CDM. Specifically, the critical disorder strength can receive a prominent change even though an arbitrarily weak Coulomb interaction is included. This novel behavior is closely related to the anisotropic screening effect of Coulomb interaction, and essentially results from the specifical energy dispersion of the fermion excitations in anisotropic Weyl semimetal. The theoretical results are helpful for understanding the physical properties of the candidates of anisotropic Weyl semimetal, such as pressured BiTeI, and some other related materials.
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Affiliation(s)
- Jing-Rong Wang
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of Anhui Province, Chinese Academy of Sciences, Hefei 230031, People's Republic of China
| | - Wei Li
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, People's Republic of China
| | - Gang Wang
- College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, People's Republic of China
| | - Chang-Jin Zhang
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of Anhui Province, Chinese Academy of Sciences, Hefei 230031, People's Republic of China
- Institute of Physical Science and Information Technology, Anhui University, Hefei 230601, People's Republic of China
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6
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Sur S, Roy B. Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling. PHYSICAL REVIEW LETTERS 2019; 123:207601. [PMID: 31809112 DOI: 10.1103/physrevlett.123.207601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2019] [Revised: 05/02/2019] [Indexed: 06/10/2023]
Abstract
We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly (d_{L}) and (at most) quadratically (d_{Q}) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative route to access various strongly interacting non-Dirac semimetals with d_{Q}>0. As a demonstrative example, we relate a two-dimensional anisotropic semimetal with d_{L}=d_{Q}=1, describing the topological transition between a Dirac semimetal and a normal insulator, and its three-dimensional counterparts with d_{L}=1, d_{Q}=2. We address the quantum critical phenomena and emergence of non-Fermi liquid states with unusual dynamical structures within the framework of an ε expansion, where ε=2-d_{Q}, when these systems reside at the brink of charge- or spin-density-wave orderings, or an s-wave pairing. Our results can be germane to two-dimensional uniaxially strained optical honeymcomb lattice, α-(BEDT-TTF)_{2}I_{3}.
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Affiliation(s)
- Shouvik Sur
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Bitan Roy
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015, USA
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7
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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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8
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Han S, Lee C, Moon EG, Min H. Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions. PHYSICAL REVIEW LETTERS 2019; 122:187601. [PMID: 31144861 DOI: 10.1103/physrevlett.122.187601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2018] [Revised: 04/04/2019] [Indexed: 06/09/2023]
Abstract
Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi-liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excitation in three spatial dimensions. Using the standard renormalization group methods, large N_{f} theory, and the ε=4-d method with a fermion flavor number N_{f} and spatial dimension d, we obtain the anomalous dimensions of electrons (η_{f}=0.366/N_{f}) in large N_{f} theory and the associated anisotropic scaling relations of various physical observables. Our results may be observed in candidate materials for DWSMs such as HgCr_{2}Se_{4} or SrSi_{2} when the system undergoes a TQPT.
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Affiliation(s)
- SangEun Han
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
| | - Changhee Lee
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
| | - Eun-Gook Moon
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
| | - Hongki Min
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
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9
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Link JM, Narozhny BN, Kiselev EI, Schmalian J. Out-of-Bounds Hydrodynamics in Anisotropic Dirac Fluids. PHYSICAL REVIEW LETTERS 2018; 120:196801. [PMID: 29799225 DOI: 10.1103/physrevlett.120.196801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2017] [Revised: 12/20/2017] [Indexed: 06/08/2023]
Abstract
We study hydrodynamic transport in two-dimensional, interacting electronic systems with merging Dirac points at charge neutrality. The dispersion along one crystallographic direction is Dirac-like, while it is Newtonian-like in the orthogonal direction. As a result, the electrical conductivity is metallic in one and insulating in the other direction. The shear viscosity tensor contains six independent components, which can be probed by measuring an anisotropic thermal flow. One of the viscosity components vanishes at zero temperature leading to a generalization of the previously conjectured lower bound for the shear viscosity to entropy density ratio.
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Affiliation(s)
- Julia M Link
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Boris N Narozhny
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow, Russia
| | - Egor I Kiselev
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Jörg Schmalian
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
- Institute for Solid State Physics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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10
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Kim J, Baik SS, Jung SW, Sohn Y, Ryu SH, Choi HJ, Yang BJ, Kim KS. Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus. PHYSICAL REVIEW LETTERS 2017; 119:226801. [PMID: 29286809 DOI: 10.1103/physrevlett.119.226801] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Indexed: 06/07/2023]
Abstract
We report the realization of novel symmetry-protected Dirac fermions in a surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely tunable band gap of black phosphorus by the surface Stark effect is employed to achieve a surprisingly large band inversion up to ∼0.6 eV. High-resolution angle-resolved photoemission spectra directly reveal the pair creation of Dirac points and their movement along the axis of the glide-mirror symmetry. Unlike graphene, the Dirac point of black phosphorus is stable, as protected by space-time inversion symmetry, even in the presence of spin-orbit coupling. Our results establish black phosphorus in the inverted regime as a simple model system of 2D symmetry-protected (topological) Dirac semimetals, offering an unprecedented opportunity for the discovery of 2D Weyl semimetals.
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Affiliation(s)
- Jimin Kim
- Department of Physics, Yonsei University, Seoul 03722, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang 37673, Korea
| | - Seung Su Baik
- Department of Physics, Yonsei University, Seoul 03722, Korea
- Center for Computational Studies of Advanced Electronic Material Properties, Yonsei University, Seoul 03722, Korea
- Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Sung Won Jung
- Department of Physics, Yonsei University, Seoul 03722, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Yeongsup Sohn
- Department of Physics, Yonsei University, Seoul 03722, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Sae Hee Ryu
- Department of Physics, Yonsei University, Seoul 03722, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
| | - Hyoung Joon Choi
- Department of Physics, Yonsei University, Seoul 03722, Korea
- Center for Computational Studies of Advanced Electronic Material Properties, Yonsei University, Seoul 03722, Korea
| | - Bohm-Jung Yang
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea
- Center for Theoretical Physics (CTS), Seoul National University, Seoul 08826, Korea
| | - Keun Su Kim
- Department of Physics, Yonsei University, Seoul 03722, Korea
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11
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Ahn J, Yang BJ. Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry. PHYSICAL REVIEW LETTERS 2017; 118:156401. [PMID: 28452536 DOI: 10.1103/physrevlett.118.156401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Indexed: 06/07/2023]
Abstract
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z_{2} topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.
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Affiliation(s)
- Junyeong Ahn
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea
- Center for Theoretical Physics (CTP), Seoul National University, Seoul 08826, Korea
| | - Bohm-Jung Yang
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea
- Center for Theoretical Physics (CTP), Seoul National University, Seoul 08826, Korea
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12
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Zhong C, Chen Y, Xie Y, Sun YY, Zhang S. Semi-Dirac semimetal in silicene oxide. Phys Chem Chem Phys 2017; 19:3820-3825. [DOI: 10.1039/c6cp08439g] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Silicene upon covalent addition of group-VI elements and strain engineering could exhibit semi-Dirac cones at the Brillouin zone center.
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Affiliation(s)
- Chengyong Zhong
- School of Physics and Optoelectronics
- Xiangtan University
- Xiangtan
- China
| | - Yuanping Chen
- School of Physics and Optoelectronics
- Xiangtan University
- Xiangtan
- China
| | - Yuee Xie
- School of Physics and Optoelectronics
- Xiangtan University
- Xiangtan
- China
| | - Yi-Yang Sun
- Department of Physics
- Applied Physics
- and Astronomy
- Rensselaer Polytechnic Institute
- Troy
| | - Shengbai Zhang
- Department of Physics
- Applied Physics
- and Astronomy
- Rensselaer Polytechnic Institute
- Troy
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13
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Hirata M, Ishikawa K, Miyagawa K, Tamura M, Berthier C, Basko D, Kobayashi A, Matsuno G, Kanoda K. Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor. Nat Commun 2016; 7:12666. [PMID: 27578363 PMCID: PMC5013692 DOI: 10.1038/ncomms12666] [Citation(s) in RCA: 100] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2015] [Accepted: 07/21/2016] [Indexed: 11/27/2022] Open
Abstract
The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.
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Affiliation(s)
- Michihiro Hirata
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
- Laboratoire National des Champs Magnétiques Intenses, UPR 3228 CNRS, EMFL, UGA, UPS and INSA, Boite Postale 166, Grenoble, Cedex 9 38042, France
| | - Kyohei Ishikawa
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Kazuya Miyagawa
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Masafumi Tamura
- Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Claude Berthier
- Laboratoire National des Champs Magnétiques Intenses, UPR 3228 CNRS, EMFL, UGA, UPS and INSA, Boite Postale 166, Grenoble, Cedex 9 38042, France
| | - Denis Basko
- Université Grenoble Alpes and CNRS, Laboratoire de Physique et Modélisation des Milieux Condensés UMR 5493, 25 rue des Martyrs, Grenoble 38042, France
| | - Akito Kobayashi
- Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
| | - Genki Matsuno
- Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
| | - Kazushi Kanoda
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
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Cho GY, Moon EG. Novel Quantum Criticality in Two Dimensional Topological Phase transitions. Sci Rep 2016; 6:19198. [PMID: 26791803 PMCID: PMC4726365 DOI: 10.1038/srep19198] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2015] [Accepted: 12/08/2015] [Indexed: 11/22/2022] Open
Abstract
Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality.
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Affiliation(s)
- Gil Young Cho
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
| | - Eun-Gook Moon
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
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