1
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Wang ZY, Liu DY, Zou LJ. Electronic instability in pressured black phosphorus under strong magnetic field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:395702. [PMID: 38906126 DOI: 10.1088/1361-648x/ad5ad4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 06/21/2024] [Indexed: 06/23/2024]
Abstract
In this paper, we have systematically studied the electronic instability of pressured black phosphorous (BP) under strong magnetic field. We first present an effective model Hamiltonian for pressured BP near theLifshitzpoint. Then we show that when the magnetic field exceeds a critical value, the nodal-line semimetal (NLSM) state of BP with a small band overlap re-enters the semiconductive phase by re-opening a small gap. This results in a narrow-bandgap semiconductor with a partially flat valence band edge. Moreover, we demonstrate that above this critical magnetic field, two possible instabilities, i.e. charge density wave phase and excitonic insulator (EI) phase, are predicted as the ground state for high and low doping concentrations, respectively. By comparing our results with the experiment (Sunet al2018Sci. Bull.631539), we suggest that the field-induced instability observed experimentally corresponds to an EI. Furthermore, we propose that the semimetallic BP under pressure with small band overlaps may provide a good platform to study the magneto-exciton insulators. Our findings bring the first insight into the electronic instability of topological NLSM in the quantum limit.
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Affiliation(s)
- Zhong-Yi Wang
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, PO Box 1129, Hefei 230031, People's Republic of China
- Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Da-Yong Liu
- Department of Physics, School of Physics and Technology, Nantong University, Nantong 226019, People's Republic of China
| | - Liang-Jian Zou
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, PO Box 1129, Hefei 230031, People's Republic of China
- Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026, People's Republic of China
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2
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Gooth J, Galeski S, Meng T. Quantum-Hall physics and three dimensions. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:044501. [PMID: 36735956 DOI: 10.1088/1361-6633/acb8c9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivityσxyof a two-dimensional electron system is exactly quantized. But what happens to the QHE in three dimensions (3D)? Experiments over the past 40 years showed that some of the remarkable physics of the QHE, in particular plateau-like Hall conductivitiesσxyaccompanied by minima in the longitudinal resistivityρxx, can also be found in 3D materials. However, since typicallyρxxremains finite and a quantitative relation betweenσxyand the conductance quantume2/hcould not be established, the role of quantum Hall physics in 3D remains unsettled. Following a recent series of exciting experiments, the QHE in 3D has now returned to the center stage. Here, we summarize the leap in understanding of 3D matter in magnetic fields emerging from these experiments.
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Affiliation(s)
- Johannes Gooth
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
- Physikalisches Institut, Rheinische Friedrich-Wilhelms-Universität, Nußalle 12, 53115 Bonn, Germany
| | - Stanislaw Galeski
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, 01187 Dresden, Germany
- Physikalisches Institut, Rheinische Friedrich-Wilhelms-Universität, Nußalle 12, 53115 Bonn, Germany
| | - Tobias Meng
- Institute of Theoretical Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, Dresden 01062, Germany
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3
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Marcenat C, Klein T, LeBoeuf D, Jaoui A, Seyfarth G, Kačmarčík J, Kohama Y, Cercellier H, Aubin H, Behnia K, Fauqué B. Wide Critical Fluctuations of the Field-Induced Phase Transition in Graphite. PHYSICAL REVIEW LETTERS 2021; 126:106801. [PMID: 33784120 DOI: 10.1103/physrevlett.126.106801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 01/28/2021] [Indexed: 06/12/2023]
Abstract
In the immediate vicinity of the critical temperature (T_{c}) of a phase transition, there are fluctuations of the order parameter that reside beyond the mean-field approximation. Such critical fluctuations usually occur in a very narrow temperature window in contrast to Gaussian fluctuations. Here, we report on a study of specific heat in graphite subject to a high magnetic field when all carriers are confined in the lowest Landau levels. The observation of a BCS-like specific heat jump in both temperature and field sweeps establishes that the phase transition discovered decades ago in graphite is of the second order. The jump is preceded by a steady field-induced enhancement of the electronic specific heat. A modest (20%) reduction in the amplitude of the magnetic field (from 33 to 27 T) leads to a threefold decrease of T_{c} and a drastic widening of the specific heat anomaly, which acquires a tail spreading to two times T_{c}. We argue that the steady departure from the mean-field BCS behavior is the consequence of an exceptionally large Ginzburg number in this dilute metal, which grows steadily as the field lowers. Our fit of the critical fluctuations indicates that they belong to the 3DXY universality class as in the case of the ^{4}He superfluid transition.
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Affiliation(s)
- Christophe Marcenat
- Université Grenoble Alpes, CEA, IRIG, PHELIQS, LATEQS, F-38000 Grenoble, France
| | - Thierry Klein
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, F-38000 Grenoble, France
| | - David LeBoeuf
- Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, UGA, UPS, INSA, 38042 Grenoble/Toulouse, France
| | - Alexandre Jaoui
- JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11, Place Marcelin Berthelot, 75231 Paris Cedex 05, France
- Laboratoire de Physique et Etude des Matériaux (CNRS/UPMC), Ecole Supérieure de Physique et de Chimie Industrielles, 10 Rue Vauquelin, 75005 Paris, France
| | - Gabriel Seyfarth
- Laboratoire National des Champs Magnétiques Intenses (LNCMI-EMFL), CNRS, UGA, UPS, INSA, 38042 Grenoble/Toulouse, France
| | - Jozef Kačmarčík
- Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, SK-04001 Košice, Slovakia
| | - Yoshimitsu Kohama
- The Institute of Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Hervé Cercellier
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, F-38000 Grenoble, France
| | - Hervé Aubin
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 91120 Palaiseau, France
| | - Kamran Behnia
- Laboratoire de Physique et Etude des Matériaux (CNRS/UPMC), Ecole Supérieure de Physique et de Chimie Industrielles, 10 Rue Vauquelin, 75005 Paris, France
| | - Benoît Fauqué
- JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11, Place Marcelin Berthelot, 75231 Paris Cedex 05, France
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4
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Wang J, Nie P, Li X, Zuo H, Fauqué B, Zhu Z, Behnia K. Critical point for Bose-Einstein condensation of excitons in graphite. Proc Natl Acad Sci U S A 2020; 117:30215-30219. [PMID: 33199600 PMCID: PMC7720211 DOI: 10.1073/pnas.2012811117] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
An exciton is an electron-hole pair bound by attractive Coulomb interaction. Short-lived excitons have been detected by a variety of experimental probes in numerous contexts. An excitonic insulator, a collective state of such excitons, has been more elusive. Here, thanks to Nernst measurements in pulsed magnetic fields, we show that in graphite there is a critical temperature (T = 9.2 K) and a critical magnetic field (B = 47 T) for Bose-Einstein condensation of excitons. At this critical field, hole and electron Landau subbands simultaneously cross the Fermi level and allow exciton formation. By quantifying the effective mass and the spatial separation of the excitons in the basal plane, we show that the degeneracy temperature of the excitonic fluid corresponds to this critical temperature. This identification would explain why the field-induced transition observed in graphite is not a universal feature of three-dimensional electron systems pushed beyond the quantum limit.
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Affiliation(s)
- Jinhua Wang
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Pan Nie
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xiaokang Li
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Huakun Zuo
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Benoît Fauqué
- Jeunes Équipes de l'Institut de Physique, Unité Mixte de Service et de Recherche 3573, CNRS, Collège de France, Paris Sciences et Lettres Research University, 75231 Paris Cedex 05, France
| | - Zengwei Zhu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China;
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Kamran Behnia
- Laboratoire de Physique et d'Étude des Matériaux, CNRS, École Supérieure de Physique et de Chimie Industrielles Paris, Paris Sciences et Lettres Research University, 75005 Paris, France
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5
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Xu S, Bao C, Guo PJ, Wang YY, Yu QH, Sun LL, Su Y, Liu K, Lu ZY, Zhou S, Xia TL. Interlayer quantum transport in Dirac semimetal BaGa 2. Nat Commun 2020; 11:2370. [PMID: 32398654 PMCID: PMC7217856 DOI: 10.1038/s41467-020-15854-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2019] [Accepted: 04/01/2020] [Indexed: 11/09/2022] Open
Abstract
The quantum limit is quite easy to achieve once the band crossing exists exactly at the Fermi level (EF) in topological semimetals. In multilayered Dirac fermion systems, the density of Dirac fermions on the zeroth Landau levels (LLs) increases in proportion to the magnetic field, resulting in intriguing angle- and field-dependent interlayer tunneling conductivity near the quantum limit. BaGa2 is an example of a multilayered Dirac semimetal with its quasi-2D Dirac cone located at EF, providing a good platform to study its interlayer transport properties. In this paper, we report the negative interlayer magnetoresistance induced by the tunneling of Dirac fermions between the zeroth LLs of neighboring Ga layers in BaGa2. When the field deviates from the c-axis, the interlayer resistivity ρzz(θ) increases and finally results in a peak with the applied field perpendicular to the c-axis. These unusual interlayer transport properties are observed together in the Dirac semimetal under ambient pressure and are well explained by the model of tunneling between Dirac fermions in the quantum limit.
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Affiliation(s)
- Sheng Xu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Changhua Bao
- State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, P. R. China
| | - Peng-Jie Guo
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Yi-Yan Wang
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Qiao-He Yu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Lin-Lin Sun
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Yuan Su
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Kai Liu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Zhong-Yi Lu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China
| | - Shuyun Zhou
- State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, P. R. China
- Collaborative Innovation Center of Quantum Matter, Beijing, P. R. China
| | - Tian-Long Xia
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing, 100872, P. R. China.
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6
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Sun Z, Xiang Z, Wang Z, Zhang J, Ma L, Wang N, Shang C, Meng F, Zou L, Zhang Y, Chen X. Magnetic field-induced electronic phase transition in the Dirac semimetal state of black phosphorus under pressure. Sci Bull (Beijing) 2018; 63:1539-1544. [PMID: 36751073 DOI: 10.1016/j.scib.2018.11.006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2018] [Revised: 11/06/2018] [Accepted: 11/13/2018] [Indexed: 11/17/2022]
Abstract
Different instabilities have been confirmed to exist in the three-dimensional (3D) electron gas when it is confined to the lowest Landau level in the extreme quantum limit. The recently discovered 3D topological semimetals offer a good platform to explore these phenomena due to the small sizes of their Fermi pockets, which means the quantum limit can be achieved at relatively low magnetic fields. In this work, we report the high-magnetic-field transport properties of the Dirac semimetal state in pressurized black phosphorus. Under applied hydrostatic pressure, the band structure of black phosphorus goes through an insulator-semimetal transition. In the high pressure topological semimetal phase, anomalous behaviors are observed on both magnetoresistance and Hall resistivity beyond the relatively low quantum limit field, which is demonstrated to indicate the emergence of an exotic electronic state hosting a density wave ordering. Our findings bring the first insight into the electronic interactions in black phosphorus under intense field.
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Affiliation(s)
- Zeliang Sun
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, and CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, University of Science and Technology of China, Hefei 230026, China
| | - Ziji Xiang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, and CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zhongyi Wang
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China
| | - Jinglei Zhang
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, and High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China
| | - Long Ma
- Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, and High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China
| | - Naizhou Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, and CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, University of Science and Technology of China, Hefei 230026, China
| | - Chao Shang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, and CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, University of Science and Technology of China, Hefei 230026, China
| | - Fanbao Meng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, and CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, University of Science and Technology of China, Hefei 230026, China
| | - Liangjian Zou
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China
| | - Yuanbo Zhang
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China; Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.
| | - Xianhui Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, and CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, University of Science and Technology of China, Hefei 230026, China; Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, and High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China; Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.
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7
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Wang H, Liu H, Li Y, Liu Y, Wang J, Liu J, Dai JY, Wang Y, Li L, Yan J, Mandrus D, Xie XC, Wang J. Discovery of log-periodic oscillations in ultraquantum topological materials. SCIENCE ADVANCES 2018; 4:eaau5096. [PMID: 30406205 PMCID: PMC6214643 DOI: 10.1126/sciadv.aau5096] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Accepted: 09/25/2018] [Indexed: 05/30/2023]
Abstract
Quantum oscillations are usually the manifestation of the underlying physical nature in condensed matter systems. Here, we report a new type of log-periodic quantum oscillations in ultraquantum three-dimensional topological materials. Beyond the quantum limit (QL), we observe the log-periodic oscillations involving up to five oscillating cycles (five peaks and five dips) on the magnetoresistance of high-quality single-crystal ZrTe5, virtually showing the clearest feature of discrete scale invariance (DSI). Further, theoretical analyses show that the two-body quasi-bound states can be responsible for the DSI feature. Our work provides a new perspective on the ground state of topological materials beyond the QL.
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Affiliation(s)
- Huichao Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Department of Applied Physics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
| | - Haiwen Liu
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Yanan Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Yongjie Liu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Junfeng Wang
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jun Liu
- Center of Electron Microscopy, State Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Ji-Yan Dai
- Department of Applied Physics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
| | - Yong Wang
- Center of Electron Microscopy, State Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China
| | - Liang Li
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jiaqiang Yan
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - David Mandrus
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA
| | - X. C. Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Jian Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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8
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Zhu Z, Fauqué B, Behnia K, Fuseya Y. Magnetoresistance and valley degree of freedom in bulk bismuth. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:313001. [PMID: 29939150 DOI: 10.1088/1361-648x/aaced7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.
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Affiliation(s)
- Zengwei Zhu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
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9
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Quantum limit transport and destruction of the Weyl nodes in TaAs. Nat Commun 2018; 9:2217. [PMID: 29880848 PMCID: PMC5992152 DOI: 10.1038/s41467-018-04542-9] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2018] [Accepted: 05/03/2018] [Indexed: 11/09/2022] Open
Abstract
Weyl fermions are a recently discovered ingredient for correlated states of electronic matter. A key difficulty has been that real materials also contain non-Weyl quasiparticles, and disentangling the experimental signatures has proven challenging. Here we use magnetic fields up to 95 T to drive the Weyl semimetal TaAs far into its quantum limit, where only the purely chiral 0th Landau levels of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 T: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 T we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral Landau levels. Above 80 T we observe strong ultrasonic attenuation below 2 K, suggesting a mesoscopically textured state of matter. These results point the way to inducing new correlated states of matter in the quantum limit of Weyl semimetals.
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10
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Thermodynamic signatures of the field-induced states of graphite. Nat Commun 2017; 8:1337. [PMID: 29116084 PMCID: PMC5677099 DOI: 10.1038/s41467-017-01394-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2016] [Accepted: 09/13/2017] [Indexed: 11/08/2022] Open
Abstract
When a magnetic field confines the carriers of a Fermi sea to their lowest Landau level, electron−electron interactions are expected to play a significant role in determining the electronic ground state. Graphite is known to host a sequence of magnetic field-induced states driven by such interactions. Three decades after their discovery, thermodynamic signatures of these instabilities are still elusive. Here we report the detection of these transitions with sound velocity measurements. The evolution of elastic constant anomalies with temperature and magnetic field allows to draw a detailed phase diagram which shows that the ground state evolves in a sequence of thermodynamic phase transitions. Our analysis indicates that the electron−electron interaction is not the sole driving force of these transitions and that lattice degrees of freedom play an important role. Previous transport studies of graphite in strong magnetic fields have found a sequence of phase transitions with a still unresolved microscopic origin. Here the authors present ultrasound measurements enabling sharper resolution and demonstrating the thermodynamic nature of these transitions.
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11
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Arnold F, Isidori A, Kampert E, Yager B, Eschrig M, Saunders J. Charge Density Waves in Graphite: Towards the Magnetic Ultraquantum Limit. PHYSICAL REVIEW LETTERS 2017; 119:136601. [PMID: 29341727 DOI: 10.1103/physrevlett.119.136601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Indexed: 06/07/2023]
Abstract
Graphite is a model system for the study of three-dimensional electrons and holes in the magnetic quantum limit, in which the charges are confined to the lowest Landau levels. We report magneto-transport measurements in pulsed magnetic fields up to 60 T, which resolve the collapse of two charge density wave states in two, electron and hole, Landau levels at 52.3 and 54.2 T, respectively. We report evidence for a commensurate charge density wave at 47.1 T in the electron Landau level, and discuss the likely nature of the density wave instabilities over the full field range. The theoretical modeling of our results predicts that the ultraquantum limit is entered above 73.5 T. This state is an insulator, and we discuss its correspondence to the "metallic" state reported earlier. We propose that this (interaction-induced) insulating phase supports surface states that carry no charge or spin within the planes, but does, however, support charge transport out of plane.
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Affiliation(s)
- F Arnold
- Royal Holloway, University of London, TW20 0EX Egham, United Kingdom
| | - A Isidori
- Royal Holloway, University of London, TW20 0EX Egham, United Kingdom
| | - E Kampert
- Hochfeld-Magnetlabor Dresden (HLD), Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany
| | - B Yager
- Royal Holloway, University of London, TW20 0EX Egham, United Kingdom
| | - M Eschrig
- Royal Holloway, University of London, TW20 0EX Egham, United Kingdom
| | - J Saunders
- Royal Holloway, University of London, TW20 0EX Egham, United Kingdom
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12
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Zhu Z, Wang J, Zuo H, Fauqué B, McDonald RD, Fuseya Y, Behnia K. Emptying Dirac valleys in bismuth using high magnetic fields. Nat Commun 2017; 8:15297. [PMID: 28524844 PMCID: PMC5454462 DOI: 10.1038/ncomms15297] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Accepted: 03/08/2017] [Indexed: 01/28/2023] Open
Abstract
The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers. A relatively small magnetic field can confine electrons to their lowest Landau level. This is the quantum limit attained in other dilute metals upon application of sufficiently strong magnetic field. Here we report on the observation of another threshold magnetic field never encountered before in any other solid. Above this field, Bempty, one or two valleys become totally empty. Drying up a Fermi sea by magnetic field in the Brillouin zone leads to a manyfold enhancement in electric conductance. We trace the origin of the large drop in magnetoresistance across Bempty to transfer of carriers between valleys with highly anisotropic mobilities. The non-interacting picture of electrons with field-dependent mobility explains most results but the Coulomb interaction may play a role in shaping the fine details.
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Affiliation(s)
- Zengwei Zhu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Jinhua Wang
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Huakun Zuo
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Benoît Fauqué
- Laboratoire Physique et Etude de Matériaux (CNRS-UPMC) ESPCI Paris, PSL Research University, Paris 75005, France.,JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11, place Marcelin Berthelot, Paris Cedex 05 75231, France
| | - Ross D McDonald
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Yuki Fuseya
- Department of Engineering Science, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan
| | - Kamran Behnia
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.,Laboratoire Physique et Etude de Matériaux (CNRS-UPMC) ESPCI Paris, PSL Research University, Paris 75005, France
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Zhu Z, McDonald RD, Shekhter A, Ramshaw BJ, Modic KA, Balakirev FF, Harrison N. Magnetic field tuning of an excitonic insulator between the weak and strong coupling regimes in quantum limit graphite. Sci Rep 2017; 7:1733. [PMID: 28496192 PMCID: PMC5431932 DOI: 10.1038/s41598-017-01693-5] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2016] [Accepted: 04/03/2017] [Indexed: 11/09/2022] Open
Abstract
The excitonic insulator phase has long been predicted to form in proximity to a band gap opening in the underlying band structure. The character of the pairing is conjectured to crossover from weak (BCS-like) to strong coupling (BEC-like) as the underlying band structure is tuned from the metallic to the insulating side of the gap opening. Here we report the high-magnetic field phase diagram of graphite to exhibit just such a crossover. By way of comprehensive angle-resolved magnetoresistance measurements, we demonstrate that the underlying band gap opening occurs inside the magnetic field-induced phase, paving the way for a systematic study of the BCS-BEC-like crossover by means of conventional condensed matter probes.
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Affiliation(s)
- Z Zhu
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA. .,Wuhan National High Magnetic Field Center, School of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, 430074, Wuhan, China.
| | - R D McDonald
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
| | - A Shekhter
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.,National High Magnetic Field Laboratory, Florida State University, 1800 E. Paul Dirac Dr., Tallahassee, Florida, 32310, USA
| | - B J Ramshaw
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.,Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, 14853, USA
| | - K A Modic
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.,Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strape 40, Presden, 01187, Germany
| | - F F Balakirev
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
| | - N Harrison
- MS-E536, NHMFL, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA.
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14
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Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5. Nat Commun 2016; 7:12516. [PMID: 27515493 PMCID: PMC4990656 DOI: 10.1038/ncomms12516] [Citation(s) in RCA: 123] [Impact Index Per Article: 15.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2016] [Accepted: 07/11/2016] [Indexed: 01/21/2023] Open
Abstract
Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-field transport measurements of the Dirac semimetal candidate ZrTe5. Owing to the large g factor in ZrTe5, the Zeeman splitting can be observed at magnetic field as low as 3 T. Most prominently, high pulsed magnetic field up to 60 T drives the system into the ultra-quantum limit, where we observe abrupt changes in the magnetoresistance, indicating field-induced phase transitions. This is interpreted as an interaction-induced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in high-energy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters.
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15
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Interplanar coupling-dependent magnetoresistivity in high-purity layered metals. Nat Commun 2016; 7:10903. [PMID: 27020134 PMCID: PMC4820545 DOI: 10.1038/ncomms10903] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2016] [Accepted: 02/01/2016] [Indexed: 11/28/2022] Open
Abstract
The magnetic field-induced changes in the conductivity of metals are the subject of intense interest, both for revealing new phenomena and as a valuable tool for determining their Fermi surface. Here we report a hitherto unobserved magnetoresistive effect in ultra-clean layered metals, namely a negative longitudinal magnetoresistance that is capable of overcoming their very pronounced orbital one. This effect is correlated with the interlayer coupling disappearing for fields applied along the so-called Yamaji angles where the interlayer coupling vanishes. Therefore, it is intrinsically associated with the Fermi points in the field-induced quasi-one-dimensional electronic dispersion, implying that it results from the axial anomaly among these Fermi points. In its original formulation, the anomaly is predicted to violate separate number conservation laws for left- and right-handed chiral (for example, Weyl) fermions. Its observation in PdCoO2, PtCoO2 and Sr2RuO4 suggests that the anomaly affects the transport of clean conductors, in particular near the quantum limit. In Weyl semimetals, unusual electronic transport phenomena are predicted to occur, such as an axial anomaly which violates the conservation of chiral fermions. Here, the authors evidence such behaviour via the occurrence of negative magnetoresistance in layered high-purity non-magnetic metals.
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Lin YP, Wang J, Lu JM, Lin CY, Lin MF. Energy spectra of ABC-stacked trilayer graphene in magnetic and electric fields. RSC Adv 2014. [DOI: 10.1039/c4ra10860d] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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17
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Arnold F, Yager B, Kampert E, Putzke C, Nyéki J, Saunders J. Spear-anvil point-contact spectroscopy in pulsed magnetic fields. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2013; 84:113901. [PMID: 24289405 DOI: 10.1063/1.4828657] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We describe a new design and experimental technique for point-contact spectroscopy in non-destructive pulsed magnetic fields up to 70 T. Point-contact spectroscopy uses a quasi-dc four-point measurement of the current and voltage across a spear-anvil point-contact. The contact resistance could be adjusted over three orders of magnitude by a built-in fine pitch threaded screw. The first measurements using this set-up were performed on both single-crystalline and exfoliated graphite samples in a 150 ms, pulse length 70 T coil at 4.2 K and reproduced the well known point-contact spectrum of graphite and showed evidence for a developing high field excitation above 35 T, the onset field of the charge-density wave instability in graphite.
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Affiliation(s)
- F Arnold
- Royal Holloway, University of London, Egham TW20 0EX, United Kingdom
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