1
|
Xu YJ, Cao G, Li QY, Xue CL, Zhao WM, Wang QW, Dou LG, Du X, Meng YX, Wang YK, Gao YH, Jia ZY, Li W, Ji L, Li FS, Zhang Z, Cui P, Xing D, Li SC. Realization of monolayer ZrTe 5 topological insulators with wide band gaps. Nat Commun 2024; 15:4784. [PMID: 38839772 PMCID: PMC11153644 DOI: 10.1038/s41467-024-49197-x] [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: 11/24/2023] [Accepted: 05/28/2024] [Indexed: 06/07/2024] Open
Abstract
Two-dimensional topological insulators hosting the quantum spin Hall effect have application potential in dissipationless electronics. To observe the quantum spin Hall effect at elevated temperatures, a wide band gap is indispensable to efficiently suppress bulk conduction. Yet, most candidate materials exhibit narrow or even negative band gaps. Here, via elegant control of van der Waals epitaxy, we have successfully grown monolayer ZrTe5 on a bilayer graphene/SiC substrate. The epitaxial ZrTe5 monolayer crystalizes in two allotrope isomers with different intralayer alignments of ZrTe3 prisms. Our scanning tunneling microscopy/spectroscopy characterization unveils an intrinsic full band gap as large as 254 meV and one-dimensional edge states localized along the periphery of the ZrTe5 monolayer. First-principles calculations further confirm that the large band gap originates from strong spin-orbit coupling, and the edge states are topologically nontrivial. These findings thus provide a highly desirable material platform for the exploration of the high-temperature quantum spin Hall effect.
Collapse
Affiliation(s)
- Yong-Jie Xu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Guohua Cao
- International Center for Quantum Design of Functional Materials (ICQD), University of Science and Technology of China, Hefei, China
| | - Qi-Yuan Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Cheng-Long Xue
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Wei-Min Zhao
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Qi-Wei Wang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Li-Guo Dou
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Xuan Du
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Yu-Xin Meng
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Yuan-Kun Wang
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Yu-Hang Gao
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Zhen-Yu Jia
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
| | - Wei Li
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou, China
| | - Lianlian Ji
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou, China
| | - Fang-Sen Li
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou, China
| | - Zhenyu Zhang
- International Center for Quantum Design of Functional Materials (ICQD), University of Science and Technology of China, Hefei, China
- Hefei National Laboratory, Hefei, China
| | - Ping Cui
- International Center for Quantum Design of Functional Materials (ICQD), University of Science and Technology of China, Hefei, China.
- Hefei National Laboratory, Hefei, China.
| | - Dingyu Xing
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Shao-Chun Li
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, China.
- Hefei National Laboratory, Hefei, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
- Jiangsu Provincial Key Laboratory for Nanotechnology, Nanjing University, Nanjing, China.
| |
Collapse
|
2
|
Xing D, Tong B, Pan S, Wang Z, Luo J, Zhang J, Zhang CL. Rashba-splitting-induced topological flat band detected by anomalous resistance oscillations beyond the quantum limit in ZrTe 5. Nat Commun 2024; 15:4407. [PMID: 38782885 PMCID: PMC11116540 DOI: 10.1038/s41467-024-48761-9] [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: 11/29/2023] [Accepted: 05/14/2024] [Indexed: 05/25/2024] Open
Abstract
Topological flat bands - where the kinetic energy of electrons is quenched - provide a platform for investigating the topological properties of correlated systems. Here, we report the observation of a topological flat band formed by polar-distortion-assisted Rashba splitting in the three-dimensional Dirac material ZrTe5. The polar distortion and resulting Rashba splitting on the band are directly detected by torque magnetometry and the anomalous Hall effect, respectively. The local symmetry breaking further flattens the band, on which we observe resistance oscillations beyond the quantum limit. These oscillations follow the temperature dependence of the Lifshitz-Kosevich formula but are evenly distributed in B instead of 1/B at high magnetic fields. Furthermore, the cyclotron mass gets anomalously enhanced about 102 times at fields ~ 20 T. Our results provide an intrinsic platform without invoking moiré or order-stacking engineering, which opens the door for studying topologically correlated phenomena beyond two dimensions.
Collapse
Affiliation(s)
- Dong Xing
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Bingbing Tong
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Senyang Pan
- High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China
| | - Zezhi Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Jianlin Luo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Jinglei Zhang
- High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China
| | - Cheng-Long Zhang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
| |
Collapse
|
3
|
Dorbath E, Gulzar A, Stock G. Log-periodic oscillations as real-time signatures of hierarchical dynamics in proteins. J Chem Phys 2024; 160:074103. [PMID: 38364004 DOI: 10.1063/5.0188220] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 01/23/2024] [Indexed: 02/18/2024] Open
Abstract
The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Examples include such diverse fields as financial crashes, random diffusion, and quantum topological materials. Recent time-resolved experiments and molecular dynamics simulations suggest that discrete scale invariance may also apply to hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur. Employing entropy-based timescale analysis and Markov state modeling to a simple one-dimensional hierarchical model and biomolecular simulation data, it is found that hierarchical systems quite generally give rise to logarithmically spaced discrete timescales. By introducing a one-dimensional reaction coordinate that collectively accounts for the hierarchically coupled degrees of freedom, the free energy landscape exhibits a characteristic staircase shape with two metastable end states, which causes the log-periodic time evolution of the system. The period of the log-oscillations reflects the effective roughness of the energy landscape and can, in simple cases, be interpreted in terms of the barriers of the staircase landscape.
Collapse
Affiliation(s)
- Emanuel Dorbath
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Adnan Gulzar
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| |
Collapse
|
4
|
Wang Y, Bömerich T, Park J, Legg HF, Taskin AA, Rosch A, Ando Y. Nonlinear Transport due to Magnetic-Field-Induced Flat Bands in the Nodal-Line Semimetal ZrTe_{5}. PHYSICAL REVIEW LETTERS 2023; 131:146602. [PMID: 37862668 DOI: 10.1103/physrevlett.131.146602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Revised: 07/11/2023] [Accepted: 09/06/2023] [Indexed: 10/22/2023]
Abstract
The Dirac material ZrTe_{5} at very low carrier density was recently found to be a nodal-line semimetal, where ultraflat bands are expected to emerge in magnetic fields parallel to the nodal-line plane. Here, we report that in very low carrier-density samples of ZrTe_{5}, when the current and the magnetic field are both along the crystallographic a axis, the current-voltage characteristics presents a pronounced nonlinearity which tends to saturate in the ultra quantum limit. The magnetic-field dependence of the nonlinear coefficient is well explained by the Boltzmann theory for flat-band transport, and we argue that this nonlinear transport is likely due to the combined effect of flat bands and charge puddles; the latter appear due to very low carrier densities.
Collapse
Affiliation(s)
- Yongjian Wang
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Thomas Bömerich
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Jinhong Park
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Henry F Legg
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - A A Taskin
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Achim Rosch
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Yoichi Ando
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| |
Collapse
|
5
|
Liu Y, Pi H, Watanabe K, Taniguchi T, Gu G, Li Q, Weng H, Wu Q, Li Y, Xu Y. Gate-Tunable Multiband Transport in ZrTe 5 Thin Devices. NANO LETTERS 2023. [PMID: 37205726 DOI: 10.1021/acs.nanolett.3c01528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Interest in ZrTe5 has been reinvigorated in recent years owing to its potential for hosting versatile topological electronic states and intriguing experimental discoveries. However, the mechanism of many of its unusual transport behaviors remains controversial: for example, the characteristic peak in the temperature-dependent resistivity and the anomalous Hall effect. Here, through employing a clean dry-transfer fabrication method in an inert environment, we successfully obtain high-quality ZrTe5 thin devices that exhibit clear dual-gate tunability and ambipolar field effects. Such devices allow us to systematically study the resistance peak as well as the Hall effect at various doping densities and temperatures, revealing the contribution from electron-hole asymmetry and multiple-carrier transport. By comparing with theoretical calculations, we suggest a simplified semiclassical two-band model to explain the experimental observations. Our work helps to resolve the longstanding puzzles on ZrTe5 and could potentially pave the way for realizing novel topological states in the two-dimensional limit.
Collapse
Affiliation(s)
- Yonghe Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Hanqi Pi
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Genda Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973-5000, United States
| | - Qiang Li
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973-5000, United States
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, United States
| | - Hongming Weng
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Quansheng Wu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yongqing Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yang Xu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| |
Collapse
|
6
|
Zhang SJ, Chen L, Li SS, Zhang Y, Yan JM, Tang F, Fang Y, Fei LF, Zhao W, Karel J, Chai Y, Zheng RK. Coexistence of logarithmic and SdH quantum oscillations in ferromagnetic Cr-doped tellurium single crystals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:245701. [PMID: 36940480 DOI: 10.1088/1361-648x/acc5ca] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Accepted: 03/20/2023] [Indexed: 06/18/2023]
Abstract
We report the synthesis of transition-metal-doped ferromagnetic elemental single-crystal semiconductors with quantum oscillations using the physical vapor transport method. The 7.7 atom% Cr-doped Te crystals (Cr:Te) show ferromagnetism, butterfly-like negative magnetoresistance in the low temperature (<3.8 K) and low field (<0.15 T) region, and high Hall mobility, e.g. 1320 cm2V-1s-1at 30 K and 350 cm2V-1s-1at 300 K, implying that Cr:Te crystals are ferromagnetic elemental semiconductors. WhenB// [001] // I, the maximum negative MR is ∼-27% atT= 20 K andB= 8 T. In the low temperature semiconducting region, Cr:Te crystals show strong discrete scale invariance dominated logarithmic quantum oscillations when the direction of the magnetic fieldBis parallel to the [100] crystallographic direction (B// [100]) and show Landau quantization dominated Shubnikov-de Haas oscillations forB// [210] direction, which suggests the broken rotation symmetry of the Fermi pockets in the Cr:Te crystals. The findings of coexistence of multiple quantum oscillations and ferromagnetism in such an elemental quantum material may inspire more study of narrow bandgap semiconductors with ferromagnetism and quantum phenomena.
Collapse
Affiliation(s)
- Shu-Juan Zhang
- School of Materials and Mechanic & Electrical Engineering, Jiangxi Science and Technology Normal University, Nanchang 330038, People's Republic of China
| | - Lei Chen
- School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, People's Republic of China
| | - Shuang-Shuang Li
- School of Materials Science and Engineering and Jiangxi Engineering Laboratory for Advanced Functional Thin Films, Nanchang University, Nanchang 330031, People's Republic of China
| | - Ying Zhang
- School of Materials Science and Engineering and Jiangxi Engineering Laboratory for Advanced Functional Thin Films, Nanchang University, Nanchang 330031, People's Republic of China
| | - Jian-Min Yan
- Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong 999077, People's Republic of China
| | - Fang Tang
- Jiangsu Laboratory of Advanced Functional Materials, Department of Physics, Changshu Institute of Technology, Changshu 215500, People's Republic of China
| | - Yong Fang
- Jiangsu Laboratory of Advanced Functional Materials, Department of Physics, Changshu Institute of Technology, Changshu 215500, People's Republic of China
| | - Lin-Feng Fei
- School of Materials Science and Engineering and Jiangxi Engineering Laboratory for Advanced Functional Thin Films, Nanchang University, Nanchang 330031, People's Republic of China
| | - Weiyao Zhao
- Department of Materials Science & Engineering, & ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Monash University, Clayton, VIC 3800, Australia
| | - Julie Karel
- Department of Materials Science & Engineering, & ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Monash University, Clayton, VIC 3800, Australia
| | - Yang Chai
- Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong 999077, People's Republic of China
| | - Ren-Kui Zheng
- School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, People's Republic of China
| |
Collapse
|
7
|
Wang J, Wu M, Zhen W, Li T, Li Y, Zhu X, Ning W, Tian M. Superconductivity in single-crystalline ZrTe 3-x ( x ≤ 0.5) nanoplates. NANOSCALE ADVANCES 2023; 5:479-484. [PMID: 36756273 PMCID: PMC9846514 DOI: 10.1039/d2na00628f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 11/17/2022] [Indexed: 06/18/2023]
Abstract
Superconductivity with an unusual filamented character below 2 K has been reported in bulk ZrTe3 crystals, a well-known charge density wave (CDW) material, but still lacks in its nanostructures. Here, we systemically investigated the transport properties of controllable chemical vapor transport synthesized ZrTe3-x nanoplates. Intriguingly, superconducting behavior is found at T c = 3.4 K and can be understood by the suppression of CDW due to the atomic disorder formed by Te vacancies. Magnetic field and angle dependent upper critical field revealed that the superconductivity in the nanoplates exhibits a large anisotropy and two-dimensional character. This two-dimensional nature of superconductivity was further satisfactorily described using the Berezinsky-Kosterlitz-Thouless transition. Our results not only demonstrate the critical role of Te vacancies for superconductivity in ZrTe3-x nanoplates, but also provide a promising platform to explore the exotic physics in the nanostructure devices.
Collapse
Affiliation(s)
- Jie Wang
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
- Department of Physics, University of Science and Technology of China Hefei 230026 P. R. China
| | - Min Wu
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
| | - Weili Zhen
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
- Department of Physics, University of Science and Technology of China Hefei 230026 P. R. China
| | - Tian Li
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
| | - Yun Li
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
- Department of Materials Science and Engineering, ARC Centre of Excellence in Future Low-Energy Electronics Technologies (FLEET), Monash University Clayton Victoria 3800 Australia
| | - Xiangde Zhu
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
| | - Wei Ning
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
| | - Mingliang Tian
- Anhui Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences Hefei 230031 Anhui P. R. China
- Department of Physics, School of Physics and Materials Science, Anhui University Hefei 230601 P. R. China
| |
Collapse
|
8
|
Wu W, Shi Z, Du Y, Wang Y, Qin F, Meng X, Liu B, Ma Y, Yan Z, Ozerov M, Zhang C, Lu HZ, Chu J, Yuan X. Topological Lifshitz transition and one-dimensional Weyl mode in HfTe 5. NATURE MATERIALS 2023; 22:84-91. [PMID: 36175521 DOI: 10.1038/s41563-022-01364-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
Landau band crossings typically stem from the intra-band evolution of electronic states in magnetic fields and enhance the interaction effect in their vicinity. Here in the extreme quantum limit of topological insulator HfTe5, we report the observation of a topological Lifshitz transition from inter-band Landau level crossings using magneto-infrared spectroscopy. By tracking the Landau level transitions, we demonstrate that band inversion drives the zeroth Landau bands to cross with each other after 4.5 T and forms a one-dimensional Weyl mode with the fundamental gap persistently closed. The unusual reduction of the zeroth Landau level transition activity suggests a topological Lifshitz transition at 21 T, which shifts the Weyl mode close to the Fermi level. As a result, a broad and asymmetric absorption feature emerges due to the Pauli blocking effect in one dimension, along with a distinctive negative magneto-resistivity. Our results provide a strategy for realizing one-dimensional Weyl quasiparticles in bulk crystals.
Collapse
Affiliation(s)
- Wenbin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Zeping Shi
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Yuhan Du
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Yuxiang Wang
- State Key Laboratory of Surface Physics and Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai, China
| | - Fang Qin
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen, China
| | - Xianghao Meng
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Binglin Liu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Yuanji Ma
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China
| | - Zhongbo Yan
- School of Physics, Sun Yat-Sen University, Guangzhou, China
| | - Mykhaylo Ozerov
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA
| | - Cheng Zhang
- State Key Laboratory of Surface Physics and Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai, China.
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China.
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China
| | - Junhao Chu
- School of Physics and Electronic Science, East China Normal University, Shanghai, China
- Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai, China
- Institute of Optoelectronics, Fudan University, Shanghai, China
| | - Xiang Yuan
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China.
- School of Physics and Electronic Science, East China Normal University, Shanghai, China.
| |
Collapse
|
9
|
Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material. Proc Natl Acad Sci U S A 2022; 119:e2204804119. [PMID: 36215510 PMCID: PMC9586292 DOI: 10.1073/pnas.2204804119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Recently, log-periodic quantum oscillations have been detected in the topological materials zirconium pentatelluride (ZrTe5) and hafnium pentatelluride (HfTe5), displaying an intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe5 can host the geometric quasi-bound states with a DSI feature, resembling an artificial supercritical atom collapse. The density of states of these quasi-bound states is enhanced, and the quasi-bound states are spatially distributed in the "orbitals" surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy. By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible; meanwhile, the energies of quasi-bound states move gradually toward the Fermi energy (EF). These features are consistent with the theoretical prediction of a magnetic field-induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.
Collapse
|
10
|
Wei W, Yang M, Jin S, Zhu H, Wang J, Han X. The current-voltage measurements under flat-top pulsed magnetic fields for non-ohmic transport study. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:085102. [PMID: 36050053 DOI: 10.1063/5.0097702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Accepted: 07/10/2022] [Indexed: 06/15/2023]
Abstract
Investigation of the non-ohmic transport behaviors under high magnetic fields can provide a new way to explore novel field-induced phenomena. We present the current-voltage measurements under high magnetic fields based on the flat-top pulsed magnetic field system. Two different measurement strategies were compared, given that the excitation current swept continuously or increased by a series of pulses. For the short duration of the flat-top pulsed field, the continuous current method was adopted and well optimized to reduce the Joule heating and achieve the quasi-static measurements. Finally, the non-ohmic behaviors of a quasi-one-dimensional charge density wave Li0.9Mo6O17 were successfully studied under the magnetic field up to 30 T at 4.2 K, which was the first current-voltage measurements carried out in pulsed magnetic fields.
Collapse
Affiliation(s)
- Wenqi Wei
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ming Yang
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Shimin Jin
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Haipeng Zhu
- 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
| | - Xiaotao Han
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| |
Collapse
|
11
|
Wang Y, Legg HF, Bömerich T, Park J, Biesenkamp S, Taskin AA, Braden M, Rosch A, Ando Y. Gigantic Magnetochiral Anisotropy in the Topological Semimetal ZrTe_{5}. PHYSICAL REVIEW LETTERS 2022; 128:176602. [PMID: 35570449 DOI: 10.1103/physrevlett.128.176602] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Revised: 02/22/2022] [Accepted: 03/31/2022] [Indexed: 06/15/2023]
Abstract
Topological materials with broken inversion symmetry can give rise to nonreciprocal responses, such as the current rectification controlled by magnetic fields via magnetochiral anisotropy. Bulk nonreciprocal responses usually stem from relativistic corrections and are always very small. Here we report our discovery that ZrTe_{5} crystals in proximity to a topological quantum phase transition present gigantic magnetochiral anisotropy, which is the largest ever observed to date. We argue that a very low carrier density, inhomogeneities, and a torus-shaped Fermi surface induced by breaking of inversion symmetry in a Dirac material are central to explain this extraordinary property.
Collapse
Affiliation(s)
- Yongjian Wang
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Henry F Legg
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Thomas Bömerich
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Jinhong Park
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Sebastian Biesenkamp
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - A A Taskin
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Markus Braden
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Achim Rosch
- Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| | - Yoichi Ando
- Physics Institute II, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany
| |
Collapse
|
12
|
Zhang R, Lv C, Yan Y, Zhou Q. Efimov-like states and quantum funneling effects on synthetic hyperbolic surfaces. Sci Bull (Beijing) 2021; 66:1967-1972. [PMID: 36654166 DOI: 10.1016/j.scib.2021.06.017] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Revised: 05/04/2021] [Accepted: 05/28/2021] [Indexed: 01/20/2023]
Abstract
Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures. Here, we point out that discrete synthetic Poincaré half-planes and Poincaré disks, which are created by lattices in flat planes, support infinitely degenerate eigenstates for any nonzero eigenenergies. Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces. Furthermore, all eigenstates are exponentially localized in the hyperbolic coordinates, signifying the first example of quantum funneling effects in Hermitian systems. As such, any initial wave packet travels towards the edge of the Poincaré half-plane or its equivalent on the Poincaré disk, delivering an efficient scheme to harvest light and atoms in two dimensions. Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.
Collapse
Affiliation(s)
- Ren Zhang
- School of Physics, Xi'an Jiaotong University, Xi'an 710049, China; Department of Physics and Astronomy, Purdue University, West Lafayette IN 47907, USA
| | - Chenwei Lv
- Department of Physics and Astronomy, Purdue University, West Lafayette IN 47907, USA
| | - Yangqian Yan
- Department of Physics and Astronomy, Purdue University, West Lafayette IN 47907, USA
| | - Qi Zhou
- Department of Physics and Astronomy, Purdue University, West Lafayette IN 47907, USA; Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette IN 47907, USA.
| |
Collapse
|
13
|
Ok JM, Mohanta N, Zhang J, Yoon S, Okamoto S, Choi ES, Zhou H, Briggeman M, Irvin P, Lupini AR, Pai YY, Skoropata E, Sohn C, Li H, Miao H, Lawrie B, Choi WS, Eres G, Levy J, Lee HN. Correlated oxide Dirac semimetal in the extreme quantum limit. SCIENCE ADVANCES 2021; 7:eabf9631. [PMID: 34524855 PMCID: PMC8443170 DOI: 10.1126/sciadv.abf9631] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 07/23/2021] [Indexed: 05/25/2023]
Abstract
Quantum materials (QMs) with strong correlation and nontrivial topology are indispensable to next-generation information and computing technologies. Exploitation of topological band structure is an ideal starting point to realize correlated topological QMs. Here, we report that strain-induced symmetry modification in correlated oxide SrNbO3 thin films creates an emerging topological band structure. Dirac electrons in strained SrNbO3 films reveal ultrahigh mobility (μmax ≈ 100,000 cm2/Vs), exceptionally small effective mass (m* ~ 0.04me), and nonzero Berry phase. Strained SrNbO3 films reach the extreme quantum limit, exhibiting a sign of fractional occupation of Landau levels and giant mass enhancement. Our results suggest that symmetry-modified SrNbO3 is a rare example of correlated oxide Dirac semimetals, in which strong correlation of Dirac electrons leads to the realization of a novel correlated topological QM.
Collapse
Affiliation(s)
- Jong Mok Ok
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | | | - Jie Zhang
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Sangmoon Yoon
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | | | - Eun Sang Choi
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA
| | - Hua Zhou
- Advanced Photon Source, Argonne National Laboratory, Lemont, IL 60439, USA
| | - Megan Briggeman
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
- Pittsburgh Quantum Institute, Pittsburgh, PA 15260, USA
| | - Patrick Irvin
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
- Pittsburgh Quantum Institute, Pittsburgh, PA 15260, USA
| | | | - Yun-Yi Pai
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | | | - Changhee Sohn
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Haoxiang Li
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Hu Miao
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | | | - Woo Seok Choi
- Department of Physics, Sungkyunkwan University, Suwon 16419, Korea
| | - Gyula Eres
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Jeremy Levy
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
- Pittsburgh Quantum Institute, Pittsburgh, PA 15260, USA
| | - Ho Nyung Lee
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| |
Collapse
|
14
|
Fu B, Wang HW, Shen SQ. Dirac Polarons and Resistivity Anomaly in ZrTe_{5} and HfTe_{5}. PHYSICAL REVIEW LETTERS 2020; 125:256601. [PMID: 33416380 DOI: 10.1103/physrevlett.125.256601] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Revised: 08/28/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
Resistivity anomaly, a sharp peak of resistivity at finite temperatures, in the transition-metal pentatellurides ZrTe_{5} and HfTe_{5} was observed four decades ago, and more exotic and anomalous behaviors of electric and thermoelectric transport were revealed in recent years. Here, we present a theory of Dirac polarons, composed by massive Dirac electrons and holes in an encircling cloud of lattice displacements or phonons at finite temperatures. The chemical potential of Dirac polarons sweeps the band gap of the topological band structure by increasing the temperature, leading to the resistivity anomaly. Formation of a nearly neutral state of Dirac polarons accounts for the anomalous behaviors of the electric and thermoelectric resistivity around the peak of resistivity.
Collapse
Affiliation(s)
- Bo Fu
- Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Huan-Wen Wang
- Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Shun-Qing Shen
- Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| |
Collapse
|
15
|
Ge J, Ma D, Liu Y, Wang H, Li Y, Luo J, Luo T, Xing Y, Yan J, Mandrus D, Liu H, Xie XC, Wang J. Unconventional Hall effect induced by Berry curvature. Natl Sci Rev 2020; 7:1879-1885. [PMID: 34691529 PMCID: PMC8288766 DOI: 10.1093/nsr/nwaa163] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2019] [Revised: 05/15/2020] [Accepted: 07/08/2020] [Indexed: 11/14/2022] Open
Abstract
Berry phase and Berry curvature play a key role in the development of topology in physics and do contribute to the transport properties in solid state systems. In this paper, we report the finding of novel nonzero Hall effect in topological material ZrTe5 flakes when the in-plane magnetic field is parallel and perpendicular to the current. Surprisingly, both symmetric and antisymmetric components with respect to magnetic field are detected in the in-plane Hall resistivity. Further theoretical analysis suggests that the magnetotransport properties originate from the anomalous velocity induced by Berry curvature in a tilted Weyl semimetal. Our work not only enriches the Hall family but also provides new insights into the Berry phase effect in topological materials.
Collapse
Affiliation(s)
- Jun Ge
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Da Ma
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Yanzhao Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Huichao Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Yanan Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Jiawei Luo
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Tianchuang Luo
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Ying Xing
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Jiaqiang Yan
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA
| | - David Mandrus
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA
| | - Haiwen Liu
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Jian Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| |
Collapse
|
16
|
Lin F, Qiao J, Huang J, Liu J, Fu D, Mayorov AS, Chen H, Mukherjee P, Qu T, Sow CH, Watanabe K, Taniguchi T, Özyilmaz B. Heteromoiré Engineering on Magnetic Bloch Transport in Twisted Graphene Superlattices. NANO LETTERS 2020; 20:7572-7579. [PMID: 32986443 DOI: 10.1021/acs.nanolett.0c03062] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Localized electrons subject to applied magnetic fields can restart to propagate freely through the lattice in delocalized magnetic Bloch states (MBSs) when the lattice periodicity is commensurate with the magnetic length. Twisted graphene superlattices with moiré wavelength tunability enable experimental access to the unique delocalization in a controllable fashion. Here, we report the observation and characterization of high-temperature Brown-Zak (BZ) oscillations which come in two types, 1/B and B periodicity, originating from the generation of integer and fractional MBSs, in the twisted bilayer and trilayer graphene superlattices, respectively. Coexisting periodic-in-1/B oscillations assigned to different moiré wavelengths are dramatically observed in small-angle twisted bilayer graphene, which may arise from angle-disorder-induced in-plane heteromoiré superlattices. Moreover, the vertical stacking of heteromoiré supercells in double-twisted trilayer graphene results in a mega-sized superlattice. The exotic superlattice contributes to the periodic-in-B oscillation and dominates the magnetic Bloch transport.
Collapse
Affiliation(s)
- Fanrong Lin
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
| | - Jiabin Qiao
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
| | - Junye Huang
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
- Department of Materials Science and Engineering, National University of Singapore, 117575, Singapore
| | - Jiawei Liu
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
| | - Deyi Fu
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
| | - Alexander S Mayorov
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
| | - Hao Chen
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
| | - Paromita Mukherjee
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
| | - Tingyu Qu
- NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, 119077, Singapore
| | - Chorng-Haur Sow
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
| | - Kenji Watanabe
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Barbaros Özyilmaz
- Centre for Advanced 2D Materials, National University of Singapore, 6 Science Drive 2, 117546, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
- Department of Materials Science and Engineering, National University of Singapore, 117575, Singapore
- NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, 119077, Singapore
| |
Collapse
|
17
|
Pazy E. Fractal geometry and the mapping of Efimov states to Bloch states. Phys Rev E 2020; 102:022136. [PMID: 32942411 DOI: 10.1103/physreve.102.022136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 08/04/2020] [Indexed: 06/11/2023]
Abstract
Efimov states are known to have a discrete real-space scale invariance; working in momentum space we identify the relevant discrete scale invariance for the scattering amplitude defining its Weierstrass function as well. Through the use of the mathematical formalism for discrete scale invariance for the scattering amplitude we identify the scaling parameters from the pole structure of the corresponding zeta function; its zeroth-order pole is fixed by the Efimov physics. The corresponding geometrical fractal structure for Efimov physics in momentum space is identified as a ray across a logarithmic spiral. This geometrical structure also appears in the physics of atomic collapse in the relativistic regime connecting it to Efimov physics. Transforming to logarithmic variables in momentum space we map the three-body scattering amplitude into Bloch states and the ladder of energies of the Efimov states are simply obtained in terms of the Bohr-Sommerfeld quantization rule. Thus through the mapping the complex problem of three-body short-range interaction is transformed to that of a noninteracting single particle in a discrete lattice.
Collapse
Affiliation(s)
- Ehoud Pazy
- Department of Physics, NRCN, P.O.B. 9001, Beer-Sheva 84190, Israel
| |
Collapse
|
18
|
Zhang N, Zhao G, Li L, Wang P, Xie L, Cheng B, Li H, Lin Z, Xi C, Ke J, Yang M, He J, Sun Z, Wang Z, Zhang Z, Zeng C. Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium. Proc Natl Acad Sci U S A 2020; 117:11337-11343. [PMID: 32398373 PMCID: PMC7260958 DOI: 10.1073/pnas.2002913117] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The study of topological materials possessing nontrivial band structures enables exploitation of relativistic physics and development of a spectrum of intriguing physical phenomena. However, previous studies of Weyl physics have been limited exclusively to semimetals. Here, via systematic magnetotransport measurements, two representative topological transport signatures of Weyl physics, the negative longitudinal magnetoresistance and the planar Hall effect, are observed in the elemental semiconductor tellurium. More strikingly, logarithmically periodic oscillations in both the magnetoresistance and Hall data are revealed beyond the quantum limit and found to share similar characteristics with those observed in ZrTe5 and HfTe5 The log-periodic oscillations originate from the formation of two-body quasi-bound states formed between Weyl fermions and opposite charge centers, the energies of which constitute a geometric series that matches the general feature of discrete scale invariance (DSI). Our discovery reveals the topological nature of tellurium and further confirms the universality of DSI in topological materials. Moreover, introduction of Weyl physics into semiconductors to develop "Weyl semiconductors" provides an ideal platform for manipulating fundamental Weyl fermionic behaviors and for designing future topological devices.
Collapse
Affiliation(s)
- Nan Zhang
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Chinese Academy of Sciences Key Laboratory of Strongly Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Gan Zhao
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Lin Li
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China;
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Chinese Academy of Sciences Key Laboratory of Strongly Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Pengdong Wang
- National Synchrotron Radiation Laboratory, University of Science and Technology of China, 230029 Hefei, Anhui, China
| | - Lin Xie
- Department of Physics, Southern University of Science and Technology, 518055 Shenzhen, China
| | - Bin Cheng
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Chinese Academy of Sciences Key Laboratory of Strongly Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Hui Li
- Institutes of Physical Science and Information Technology, Anhui University, 230601 Hefei, Anhui, China
| | - Zhiyong Lin
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Chinese Academy of Sciences Key Laboratory of Strongly Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Chuanying Xi
- High Magnetic Field Laboratory, Chinese Academy of Sciences, 230031 Hefei, Anhui, China
| | - Jiezun Ke
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, 430074 Wuhan, China
| | - Ming Yang
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, 430074 Wuhan, China
| | - Jiaqing He
- Department of Physics, Southern University of Science and Technology, 518055 Shenzhen, China
| | - Zhe Sun
- National Synchrotron Radiation Laboratory, University of Science and Technology of China, 230029 Hefei, Anhui, China
| | - Zhengfei Wang
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China;
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Zhenyu Zhang
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| | - Changgan Zeng
- International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 230026 Hefei, Anhui, China;
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
- Chinese Academy of Sciences Key Laboratory of Strongly Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, 230026 Hefei, Anhui, China
| |
Collapse
|
19
|
Bhoyar PD, Gade PM. Dynamic phase transition in the contact process with spatial disorder: Griffiths phase and complex persistence exponents. Phys Rev E 2020; 101:022128. [PMID: 32168682 DOI: 10.1103/physreve.101.022128] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2019] [Accepted: 01/30/2020] [Indexed: 11/07/2022]
Abstract
We present a model which displays the Griffiths phase, i.e., algebraic decay of density with continuously varying exponents in the absorbing phase. In the active phase, the memory of initial conditions is lost with continuously varying complex exponents in this model. This is a one-dimensional model where a fraction r of sites obey rules leading to the directed percolation class and the rest evolve according to rules leading to the compact directed percolation class. For infection probability p≤p_{c}, the fraction of active sites ρ(t)=0 asymptotically. For p>p_{c}, ρ(∞)>0. At p=p_{c}, ρ(t), the survival probability from a single seed and the average number of active sites starting from single seed decay logarithmically. The local persistence P_{l}(∞)>0 for p≤p_{c} and P_{l}(∞)=0 for p>p_{c}. For p≥p_{s}, local persistence P_{l}(t) decays as a power law with continuously varying exponents. The persistence exponent is clearly complex as p→1. The complex exponent implies logarithmic periodic oscillations in persistence. The wavelength and the amplitude of the logarithmic periodic oscillations increase with p. We note that the underlying lattice or disorder does not have a self-similar structure.
Collapse
Affiliation(s)
- Priyanka D Bhoyar
- Department of Physics, Seth Kesarimal Porwal College of Arts and Science and Commerce, Kamptee 441 001, India
| | - Prashant M Gade
- Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India
| |
Collapse
|
20
|
Wang H, Liu Y, Liu Y, Xi C, Wang J, Liu J, Wang Y, Li L, Lau SP, Tian M, Yan J, Mandrus D, Dai JY, Liu H, Xie X, Wang J. Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe 5. Natl Sci Rev 2019; 6:914-920. [PMID: 34691952 PMCID: PMC8291527 DOI: 10.1093/nsr/nwz110] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Revised: 07/28/2019] [Accepted: 07/28/2019] [Indexed: 11/14/2022] Open
Abstract
Discrete-scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity that can be rarely observed in quantum systems. Here, we report the log-periodic quantum oscillations in the longitudinal magnetoresistivity (ρxx ) and the Hall traces (ρyx ) of HfTe5 crystals, which reveal the DSI in the transport-coefficients matrix. The oscillations in ρxx and ρyx show the consistent logB-periodicity with a phase shift. The finding of the logB oscillations in the Hall resistance supports the physical mechanism as a general quantum effect originating from the resonant scattering. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. This work evidences the universality of the DSI in the Dirac materials and provides indispensable information for a full understanding of this novel phenomenon.
Collapse
Affiliation(s)
- Huichao Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, China
| | - Yanzhao Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Yongjie Liu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Chuanying Xi
- High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, 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
| | - 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
| | - Shu Ping Lau
- Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, China
| | - Mingliang Tian
- High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, 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
| | - Ji-Yan Dai
- Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, China
| | - Haiwen Liu
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Xincheng 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
- Beijing Academy of Quantum Information Sciences, Beijing 100193, 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
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| |
Collapse
|
21
|
Wang H, Chan CH, Suen CH, Lau SP, Dai JY. Magnetotransport Properties of Layered Topological Material ZrTe 2 Thin Film. ACS NANO 2019; 13:6008-6016. [PMID: 31013050 DOI: 10.1021/acsnano.9b02196] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
ZrTe2 is a candidate topological material from the layered two-dimensional transition-metal dichalcogenide family, and thus the material may show exotic electrical transport properties and may be promising for quantum device applications. In this work, we report the successful growth of layered ZrTe2 thin film by pulsed-laser deposition and the experimental results of its magnetotransport properties. In the presence of a perpendicular magnetic field, the 60 nm thick ZrTe2 film shows a large magnetoresistance of 3000% at 2 K and 9 T. A robust linear magnetoresistance is observed under an in-plane magnetic field, and negative magnetoresistance appears in the film when the magnetic field is parallel to the current direction. Furthermore, the Hall results reveal that the ZrTe2 thin film has a high electron mobility of about 1.8 × 104 cm2 V-1 s-1 at 2 K. These findings provide insights into further investigations and potential applications of this layered topological material system.
Collapse
Affiliation(s)
- Huichao Wang
- Department of Applied Physics , The Hong Kong Polytechnic University , Hung Hom, Kowloon , Hong Kong, P.R. China
| | - Cheuk Ho Chan
- Department of Applied Physics , The Hong Kong Polytechnic University , Hung Hom, Kowloon , Hong Kong, P.R. China
| | - Chun Hung Suen
- Department of Applied Physics , The Hong Kong Polytechnic University , Hung Hom, Kowloon , Hong Kong, P.R. China
| | - Shu Ping Lau
- Department of Applied Physics , The Hong Kong Polytechnic University , Hung Hom, Kowloon , Hong Kong, P.R. China
| | - Ji-Yan Dai
- Department of Applied Physics , The Hong Kong Polytechnic University , Hung Hom, Kowloon , Hong Kong, P.R. China
| |
Collapse
|
22
|
Wang Z. Quantum oscillations turn log( B )-periodic in Dirac semimetals: ‘Who ordered that?’. Natl Sci Rev 2019; 6:378-379. [PMID: 34691878 PMCID: PMC8291426 DOI: 10.1093/nsr/nwz016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
|
23
|
Zhang P, Zhai H. Scaling symmetry meets topology. Sci Bull (Beijing) 2019; 64:289-290. [PMID: 36659590 DOI: 10.1016/j.scib.2019.02.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Pengfei Zhang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
| |
Collapse
|
24
|
Affiliation(s)
- Jian Wang
- International Center for Quantum Materials, School of Physics, Peking University, China
- Collaborative Innovation Center of Quantum Matter, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, China
- Beijing Academy of Quantum Information Sciences, China
| |
Collapse
|
25
|
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.
Collapse
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.
| |
Collapse
|