1
|
Zhuo D, Zhou L, Zhao YF, Zhang R, Yan ZJ, Wang AG, Chan MHW, Liu CX, Chen CZ, Chang CZ. Engineering Plateau Phase Transition in Quantum Anomalous Hall Multilayers. NANO LETTERS 2024; 24:6974-6980. [PMID: 38829211 DOI: 10.1021/acs.nanolett.4c01313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2024]
Abstract
The plateau phase transition in quantum anomalous Hall (QAH) insulators corresponds to a quantum state wherein a single magnetic domain gives way to multiple domains and then reconverges back to a single magnetic domain. The layer structure of the sample provides an external knob for adjusting the Chern number C of the QAH insulators. Here, we employ molecular beam epitaxy to grow magnetic topological insulator multilayers and realize the magnetic field-driven plateau phase transition between two QAH states with odd Chern number change ΔC. We find that critical exponents extracted for the plateau phase transitions with ΔC = 1 and ΔC = 3 in QAH insulators are nearly identical. We construct a four-layer Chalker-Coddington network model to understand the consistent critical exponents for the plateau phase transitions with ΔC = 1 and ΔC = 3. This work will motivate further investigations into the critical behaviors of plateau phase transitions with different ΔC in QAH insulators.
Collapse
Affiliation(s)
- Deyi Zhuo
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Lingjie Zhou
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Yi-Fan Zhao
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Ruoxi Zhang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Zi-Jie Yan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Annie G Wang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Moses H W Chan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Chao-Xing Liu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Chui-Zhen Chen
- Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Cui-Zu Chang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| |
Collapse
|
2
|
Wang Z, Liu Y, Ji C, Wang J. Quantum phase transitions in two-dimensional superconductors: a review on recent experimental progress. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 87:014502. [PMID: 38086096 DOI: 10.1088/1361-6633/ad14f3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Accepted: 12/12/2023] [Indexed: 12/30/2023]
Abstract
Superconductor-insulator/metal transition (SMT) as a paradigm of quantum phase transition has been a research highlight over the last three decades. Benefit from recent developments in the fabrication and measurements of two-dimensional (2D) superconducting films and nanodevices, unprecedented quantum phenomena have been revealed in the quantum phase transitions of 2D superconductors. In this review, we introduce the recent progress on quantum phase transitions in 2D superconductors, focusing on the quantum Griffiths singularity (QGS) and anomalous metal state. Characterized by a divergent critical exponent when approaching zero temperature, QGS of SMT is discovered in ultrathin crystalline Ga films and subsequently detected in various 2D superconductors. The universality of QGS indicates the profound influence of quenched disorder on quantum phase transitions. Besides, in a 2D superconducting system, whether a metallic ground state can exist is a long-sought mystery. Early experimental studies indicate an intermediate metallic state in the quantum phase transition of 2D superconductors. Recently, in high-temperature superconducting films with patterned nanopores, a robust anomalous metal state (i.e. quantum metal or Bose metal) has been detected, featured as the saturated resistance in the low temperature regime. Moreover, the charge-2equantum oscillations are observed in nanopatterned films, indicating the bosonic nature of the anomalous metal state and ending the debate on whether bosons can exist as a metal. The evidences of the anomalous metal states have also been reported in crystalline epitaxial thin films and exfoliated nanoflakes, as well as granular composite films. High quality filters are used in these works to exclude the influence of external high frequency noises in ultralow temperature measurements. The observations of QGS and metallic ground states in 2D superconductors not only reveal the prominent role of quantum fluctuations and dissipations but also provide new perspective to explore quantum phase transitions in superconducting systems.
Collapse
Affiliation(s)
- Ziqiao Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Yi Liu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, People's Republic of China
- Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, People's Republic of China
| | - Chengcheng Ji
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
| | - Jian Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People's Republic of China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| |
Collapse
|
3
|
Madathil PT, Villegas Rosales KA, Tai CT, Chung YJ, Pfeiffer LN, West KW, Baldwin KW, Shayegan M. Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions. PHYSICAL REVIEW LETTERS 2023; 130:226503. [PMID: 37327438 DOI: 10.1103/physrevlett.130.226503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 05/12/2023] [Indexed: 06/18/2023]
Abstract
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent κ≃0.42. Here we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our Letter is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that κ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor ν=1/2 and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the nonuniversal κ observed in our experiments.
Collapse
Affiliation(s)
- P T Madathil
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K A Villegas Rosales
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - C T Tai
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Y J Chung
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - L N Pfeiffer
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W West
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - K W Baldwin
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - M Shayegan
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
4
|
Luan J, Feng Y, Ji Y, Li Y, Li H, Liu Z, Liu C, Zhang J, Kou X, Wang Y. Controlling the Zero Hall Plateau in a Quantum Anomalous Hall Insulator by In-Plane Magnetic Field. PHYSICAL REVIEW LETTERS 2023; 130:186201. [PMID: 37204911 DOI: 10.1103/physrevlett.130.186201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2022] [Accepted: 04/07/2023] [Indexed: 05/21/2023]
Abstract
We investigate the quantum anomalous Hall plateau transition in the presence of independent out-of-plane and in-plane magnetic fields. The perpendicular coercive field, zero Hall plateau width, and peak resistance value can all be systematically controlled by the in-plane magnetic field. The traces taken at various fields almost collapse into a single curve when the field vector is renormalized to an angle as a geometric parameter. These results can be explained consistently by the competition between magnetic anisotropy and in-plane Zeeman field, and the close relationship between quantum transport and magnetic domain structure. The accurate control of zero Hall plateau facilitates the search for chiral Majorana modes based on the quantum anomalous Hall system in proximity to a superconductor.
Collapse
Affiliation(s)
- Jianli Luan
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yang Feng
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People's Republic of China
| | - Yuchen Ji
- ShanghaiTech Laboratory for Topological Physics, School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, People's Republic of China
| | - Yuanzhao Li
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Hangzhe Li
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Zhongkai Liu
- ShanghaiTech Laboratory for Topological Physics, School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, People's Republic of China
| | - Chang Liu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People's Republic of China
| | - Jinsong Zhang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Frontier Science Center for Quantum Information, Beijing 100084, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
| | - Xufeng Kou
- ShanghaiTech Laboratory for Topological Physics, School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, People's Republic of China
- School of Information Science and Technology, ShanghaiTech University, Shanghai 20031, People's Republic of China
| | - Yayu Wang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Frontier Science Center for Quantum Information, Beijing 100084, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
| |
Collapse
|
5
|
Deng P, Eckberg C, Zhang P, Qiu G, Emmanouilidou E, Yin G, Chong SK, Tai L, Ni N, Wang KL. Probing the mesoscopic size limit of quantum anomalous Hall insulators. Nat Commun 2022; 13:4246. [PMID: 35869045 PMCID: PMC9307791 DOI: 10.1038/s41467-022-31105-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Accepted: 06/06/2022] [Indexed: 11/09/2022] Open
Abstract
The inelastic scattering length (Ls) is a length scale of fundamental importance in condensed matters due to the relationship between inelastic scattering and quantum dephasing. In quantum anomalous Hall (QAH) materials, the mesoscopic length scale Ls plays an instrumental role in determining transport properties. Here we examine Ls in three regimes of the QAH system with distinct transport behaviors: the QAH, quantum critical, and insulating regimes. Although the resistance changes by five orders of magnitude when tuning between these distinct electronic phases, scaling analyses indicate a universal Ls among all regimes. Finally, mesoscopic scaled devices with sizes on the order of Ls were fabricated, enabling the direct detection of the value of Ls in QAH samples. Our results unveil the fundamental length scale that governs the transport behavior of QAH materials. In quantum anomalous Hall (QAH) materials, the mesoscopic scattering length (Ls) plays an instrumental role in determining transport properties. Here, the authors examine Ls in three regimes (QAH, quantum critical, and insulating) with distinct transport behaviours, and find a universal Ls across all regimes.
Collapse
|
6
|
Zhao YF, Zhang R, Zhou LJ, Mei R, Yan ZJ, Chan MHW, Liu CX, Chang CZ. Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators. PHYSICAL REVIEW LETTERS 2022; 128:216801. [PMID: 35687436 DOI: 10.1103/physrevlett.128.216801] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 05/06/2022] [Indexed: 06/15/2023]
Abstract
The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states. It can be achieved by either sweeping the magnetic field or tuning the carrier density. The recent realization of the quantum anomalous Hall (QAH) insulators with tunable Chern numbers introduces the channel degree of freedom to the dissipation-free chiral edge transport and makes the study of the quantum phase transition between two topological states under zero magnetic field possible. Here, we synthesized the magnetic topological insulator (TI)/TI pentalayer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy. By performing transport measurements, we found a potential plateau phase transition between C=1 and C=2 QAH states under zero magnetic field. In tuning the transition, the Hall resistance monotonically decreases from h/e^{2} to h/2e^{2}, concurrently, the longitudinal resistance exhibits a maximum at the critical point. Our results show that the ratio between the Hall resistance and the longitudinal resistance is greater than 1 at the critical point, which indicates that the original chiral edge channel from the C=1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels appear to self-organize and form the second chiral edge channel in completing the plateau phase transition. Our study will motivate further investigations of this novel Chern number change-induced quantum phase transition and advance the development of the QAH chiral edge current-based electronic and spintronic devices.
Collapse
Affiliation(s)
- Yi-Fan Zhao
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Ruoxi Zhang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Ling-Jie Zhou
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Ruobing Mei
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Zi-Jie Yan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Moses H W Chan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Chao-Xing Liu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Cui-Zu Chang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| |
Collapse
|
7
|
Huang KS, Raghu S, Kumar P. Numerical Study of a Dual Representation of the Integer Quantum Hall Transition. PHYSICAL REVIEW LETTERS 2021; 126:056802. [PMID: 33605754 DOI: 10.1103/physrevlett.126.056802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
We study the critical properties of the noninteracting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality CF states are delocalized at all energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain ν=2.56±0.02 and η=0.51±0.01, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.
Collapse
Affiliation(s)
- Kevin S Huang
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - S Raghu
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Prashant Kumar
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
8
|
Wu X, Xiao D, Chen CZ, Sun J, Zhang L, Chan MHW, Samarth N, Xie XC, Lin X, Chang CZ. Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator. Nat Commun 2020; 11:4532. [PMID: 32913228 PMCID: PMC7483742 DOI: 10.1038/s41467-020-18312-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Accepted: 08/18/2020] [Indexed: 11/08/2022] Open
Abstract
The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker-Coddington network model. We extract a critical exponent κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker-Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33.
Collapse
Affiliation(s)
- Xinyu Wu
- International Center for Quantum Materials, Peking University, Beijing, 100871, China
| | - Di Xiao
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Chui-Zhen Chen
- Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou, 215006, China
| | - Jian Sun
- International Center for Quantum Materials, Peking University, Beijing, 100871, China
| | - Ling Zhang
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Moses H W Chan
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Nitin Samarth
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | - X C Xie
- International Center for Quantum Materials, Peking University, Beijing, 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing, 100871, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, 100190, China.
| | - Cui-Zu Chang
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA.
| |
Collapse
|
9
|
Ippoliti M, Bhatt RN. Dimensional Crossover of the Integer Quantum Hall Plateau Transition and Disordered Topological Pumping. PHYSICAL REVIEW LETTERS 2020; 124:086602. [PMID: 32167341 DOI: 10.1103/physrevlett.124.086602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
We study the quantum Hall plateau transition on rectangular tori. As the aspect ratio of the torus is increased, the two-dimensional critical behavior, characterized by a subthermodynamic number of topological states in a vanishing energy window around a critical energy, changes drastically. In the thin-torus limit, the entire spectrum is Anderson localized; however, an extensive number of states retain a Chern number C≠0. We resolve this apparent paradox by mapping the thin-torus quantum Hall system onto a disordered Thouless pump, where the Chern number corresponds to the winding number of an electron's path in real space during a pump cycle. We then characterize quantitatively the crossover between the one- and two-dimensional regimes for finite torus thickness, where the average Thouless conductance also shows anomalous scaling.
Collapse
Affiliation(s)
- Matteo Ippoliti
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - R N Bhatt
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
10
|
Sela E, Bloch Y, von Oppen F, Shalom MB. Quantum Hall Response to Time-Dependent Strain Gradients in Graphene. PHYSICAL REVIEW LETTERS 2020; 124:026602. [PMID: 32004059 DOI: 10.1103/physrevlett.124.026602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Indexed: 06/10/2023]
Abstract
Mechanical deformations of graphene induce a term in the Dirac Hamiltonian that is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time-dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detail a particular experimental implementation in the (pseudo)quantum Hall regime with weak intervalley scattering. This allows us to predict an (approximately) quantized Hall current that is unaffected by screening due to diffusion currents.
Collapse
Affiliation(s)
- Eran Sela
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, IL-69978 Tel Aviv, Israel
| | - Yakov Bloch
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, IL-69978 Tel Aviv, Israel
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Moshe Ben Shalom
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, IL-69978 Tel Aviv, Israel
| |
Collapse
|
11
|
Liu Z, Bhatt RN. Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids. PHYSICAL REVIEW LETTERS 2016; 117:206801. [PMID: 27886478 DOI: 10.1103/physrevlett.117.206801] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2016] [Indexed: 06/06/2023]
Abstract
We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder-the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase.
Collapse
Affiliation(s)
- Zhao Liu
- Dahlem Center for Complex Quantum Systems and Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - R N Bhatt
- Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
| |
Collapse
|
12
|
Chang CZ, Li M. Quantum anomalous Hall effect in time-reversal-symmetry breaking topological insulators. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:123002. [PMID: 26934535 DOI: 10.1088/0953-8984/28/12/123002] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The quantum anomalous Hall effect (QAHE), the last member of Hall family, was predicted to exhibit quantized Hall conductivity σ(yx) = e2/h without any external magnetic field. The QAHE shares a similar physical phenomenon with the integer quantum Hall effect (QHE), whereas its physical origin relies on the intrinsic topological inverted band structure and ferromagnetism. Since the QAHE does not require external energy input in the form of magnetic field, it is believed that this effect has unique potential for applications in future electronic devices with low-power consumption. More recently, the QAHE has been experimentally observed in thin films of the time-reversal symmetry breaking ferromagnetic (FM) topological insulators (TI), Cr- and V- doped (Bi,Sb)2Te3. In this topical review, we review the history of TI based QAHE, the route to the experimental observation of the QAHE in the above two systems, the current status of the research of the QAHE, and finally the prospects for future studies.
Collapse
Affiliation(s)
- Cui-Zu Chang
- Francis Bitter Magnet Lab, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | |
Collapse
|
13
|
Kou X, Pan L, Wang J, Fan Y, Choi ES, Lee WL, Nie T, Murata K, Shao Q, Zhang SC, Wang KL. Metal-to-insulator switching in quantum anomalous Hall states. Nat Commun 2015; 6:8474. [PMID: 26442609 PMCID: PMC4633736 DOI: 10.1038/ncomms9474] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2015] [Accepted: 08/25/2015] [Indexed: 12/23/2022] Open
Abstract
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr0.12Bi0.26Sb0.62)2Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. In addition, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications. The quantum anomalous Hall effect is a recently demonstrated chiral transport phenomenon arising in magnetically doped topological insulators. Here, the authors study the Hall plateau switching and universal phase diagram of the quantum anomalous Hall effect in thin films of two-dimensional Cr-doped (BiSb)2Te3.
Collapse
Affiliation(s)
- Xufeng Kou
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Lei Pan
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Jing Wang
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Yabin Fan
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Eun Sang Choi
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310-3706, USA
| | - Wei-Li Lee
- Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
| | - Tianxiao Nie
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Koichi Murata
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Qiming Shao
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Shou-Cheng Zhang
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Kang L Wang
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| |
Collapse
|
14
|
Dodoo-Amoo NA, Saeed K, Mistry D, Khanna SP, Li L, Linfield EH, Davies AG, Cunningham JE. Non-universality of scaling exponents in quantum Hall transitions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:475801. [PMID: 25351842 DOI: 10.1088/0953-8984/26/47/475801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We have investigated experimentally the scaling behaviour of quantum Hall transitions in GaAs/AlGaAs heterostructures of a range of mobility, carrier concentration, and spacer layer width. All three critical scaling exponents γ, κ and p were determined independently for each sample. We measure the localization length exponent to be γ ≈ 2.3, in good agreement with expected predictions from scaling theory, but κ and p are found to possess non-universal values. Results obtained for κ range from κ = 0.16 ± 0.02 to κ = 0.67 ± 0.02, and are found to be Landau level (LL) dependent, whereas p is found to decrease with increasing sample mobility. Our results demonstrate the existence of two transport regimes in the LL conductivity peak; universality is found within the quantum coherent transport regime present in the tails of the conductivity peak, but is absent within the classical transport regime found close to the critical point at the centre of the conductivity peak. We explain these results using a percolation model and show that the critical scaling exponent depends on certain important length scales that correspond to the microscopic description of electron transport in the bulk of a two-dimensional electron system.
Collapse
Affiliation(s)
- N A Dodoo-Amoo
- School of Electronic and Electrical Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT,UK
| | | | | | | | | | | | | | | |
Collapse
|
15
|
Wang YT, Kim GH, Huang CF, Lo ST, Chen WJ, Nicholls JT, Lin LH, Ritchie DA, Chang YH, Liang CT, Dolan BP. Probing temperature-driven flow lines in a gated two-dimensional electron gas with tunable spin-splitting. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:405801. [PMID: 22968970 DOI: 10.1088/0953-8984/24/40/405801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We study the temperature flow of conductivities in a gated GaAs two-dimensional electron gas (2DEG) containing self-assembled InAs dots and compare the results with recent theoretical predictions. By changing the gate voltage, we are able to tune the 2DEG density and thus vary disorder and spin-splitting. Data for both the spin-resolved and spin-degenerate phase transitions are presented, the former collapsing to the latter with decreasing gate voltage and/or decreasing spin-splitting. The experimental results support a recent theory, based on modular symmetry, which predicts how the critical Hall conductivity varies with spin-splitting.
Collapse
Affiliation(s)
- Yi-Ting Wang
- Department of Physics, National Taiwan University, Taipei 106, Taiwan
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
16
|
Amado M, Diez E, Rossella F, Bellani V, López-Romero D, Maude DK. Magneto-transport of graphene and quantum phase transitions in the quantum Hall regime. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:305302. [PMID: 22771627 DOI: 10.1088/0953-8984/24/30/305302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
In this paper we show the electronic transport and the quantum phase transitions that characterize the quantum Hall regime in graphene placed on SiO(2) substrates at magnetic fields up to 28 T and temperatures down to 4 K. The analysis of the temperature dependence of the Hall and longitudinal resistivity reveals intriguing non-universalities of the critical exponents of the plateau-insulator transition. These exponents depend on the type of disorder that governs the electrical transport and its characterization is important for the design and fabrication of novel graphene nano-devices.
Collapse
Affiliation(s)
- Mario Amado
- Laboratorio de Bajas Temperaturas, Universidad de Salamanca, 37008 Salamanca, Spain.
| | | | | | | | | | | |
Collapse
|
17
|
Lopez M, Clément JF, Szriftgiser P, Garreau JC, Delande D. Experimental test of universality of the Anderson transition. PHYSICAL REVIEW LETTERS 2012; 108:095701. [PMID: 22463648 DOI: 10.1103/physrevlett.108.095701] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2011] [Indexed: 05/31/2023]
Abstract
We experimentally test the universality of the Anderson three dimensional metal-insulator transition, using a quasiperiodic atomic kicked rotor. Nine sets of parameters controlling the microscopic details have been tested. Our observation indicates that the transition is of second order, with a critical exponent independent of the microscopic details; the average value 1.63±0.05 agrees very well with the numerically predicted value ν=1.58.
Collapse
Affiliation(s)
- Matthias Lopez
- Laboratoire de Physique des Lasers, Atomes et Molécules, Université Lille 1 Sciences et Technologies, CNRS; F-59655 Villeneuve d'Ascq Cedex, France
| | | | | | | | | |
Collapse
|
18
|
|
19
|
Ikebe Y, Morimoto T, Masutomi R, Okamoto T, Aoki H, Shimano R. Optical Hall effect in the integer quantum Hall regime. PHYSICAL REVIEW LETTERS 2010; 104:256802. [PMID: 20867407 DOI: 10.1103/physrevlett.104.256802] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2010] [Indexed: 05/29/2023]
Abstract
Optical Hall conductivity σ{xy}(ω) is measured from the Faraday rotation for a GaAs/AlGaAs heterojunction quantum Hall system in the terahertz-frequency regime. The Faraday rotation angle (∼ fine-structure constant ∼ mrad) is found to significantly deviate from the Drude-like behavior to exhibit a plateaulike structure around the Landau-level filling ν=2. The result, which fits with the behavior expected from the carrier localization effect in the ac regime, indicates that the plateau structure, although not quantized, still exists in the terahertz regime.
Collapse
Affiliation(s)
- Y Ikebe
- Department of Physics, The University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | | | | | | | | | | |
Collapse
|
20
|
Li W, Vicente CL, Xia JS, Pan W, Tsui DC, Pfeiffer LN, West KW. Scaling in plateau-to-plateau transition: a direct connection of quantum hall systems with the Anderson localization model. PHYSICAL REVIEW LETTERS 2009; 102:216801. [PMID: 19519123 DOI: 10.1103/physrevlett.102.216801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2005] [Indexed: 05/27/2023]
Abstract
The quantum Hall-plateau transition was studied at temperatures down to 1 mK in a random alloy disordered high mobility two-dimensional electron gas. A perfect power-law scaling with kappa=0.42 was observed from 1.2 K down to 12 mK. This perfect scaling terminates sharply at a saturation temperature of Ts approximately 10 mK. The saturation is identified as a finite-size effect when the quantum phase coherence length (Lphi proportional, T(-p/2)) reaches the sample size (W) of millimeter scale. From a size dependent study, Ts proportional, W(-1) was observed and p=2 was obtained. The exponent of the localization length, determined directly from the measured kappa and p, is nu=2.38, and the dynamic critical exponent z=1.
Collapse
Affiliation(s)
- Wanli Li
- Princeton University, Princeton, New Jersey 08544, USA.
| | | | | | | | | | | | | |
Collapse
|
21
|
Pusep YA, Rodriguez A, Arakaki AH, de Souza CA. Influence of interlayer tunneling on the quantized Hall phases in intentionally disordered multilayer structures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:205501. [PMID: 21825531 DOI: 10.1088/0953-8984/21/20/205501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Stability of the quantized Hall phases is studied in weakly coupled multilayers as a function of the interlayer correlations controlled by the interlayer tunneling and by the random variation of the well thicknesses. A strong enough interlayer disorder destroys the symmetry responsible for the quantization of the Hall conductivity, resulting in the breakdown of the quantum Hall effect. A clear difference between the dimensionalities of the metallic and insulating quantum Hall phases is demonstrated. The sharpness of the quantized Hall steps obtained in the coupled multilayers with different degrees of randomization was found consistent with the calculated interlayer tunneling energies. The observed width of the transition between the quantized Hall states in random multilayers is explained in terms of the local fluctuations of the electron density.
Collapse
Affiliation(s)
- Yu A Pusep
- Instituto de Fisica de São Carlos, Universidade de São Paulo, 13460-970 São Carlos, SP, Brazil
| | | | | | | |
Collapse
|
22
|
Visser AD, Ponomarenko LA, Galistu G, Lang DTND, Pruisken AMM, Zeitler U, Maude D. Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/1742-6596/51/1/088] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
23
|
Murakami S. Quantum spin Hall effect and enhanced magnetic response by spin-orbit coupling. PHYSICAL REVIEW LETTERS 2006; 97:236805. [PMID: 17280226 DOI: 10.1103/physrevlett.97.236805] [Citation(s) in RCA: 180] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2006] [Indexed: 05/13/2023]
Abstract
We show that the spin-Hall conductivity in insulators is related to a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin-Hall effect. As a result, we theoretically predict that two-dimensional bismuth will show the quantum spin-Hall effect, both by calculating the helical edge states, and by showing the nontriviality of the Z2 topological number, and propose possible experiments.
Collapse
Affiliation(s)
- Shuichi Murakami
- Department of Applied Physics, University of Tokyo, Hongo, Tokyo 113-8656, Japan.
| |
Collapse
|
24
|
Struck A, Kramer B. Electron correlations and single-particle physics in the integer quantum Hall effect. PHYSICAL REVIEW LETTERS 2006; 97:106801. [PMID: 17025841 DOI: 10.1103/physrevlett.97.106801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2005] [Indexed: 05/12/2023]
Abstract
The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical results for the influences of interaction and disorder on the compressibility as a function of the particle density and the strength of the magnetic field are presented. Localization-delocalization transitions associated with a highly compressible region in the energy spectrum are found at half-integer filling factors. Coulomb blockade effects are found near integer fillings in the regions of low compressibility. Results are compared with recent experiments.
Collapse
Affiliation(s)
- Alexander Struck
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstrasse 9, 20355 Hamburg, Germany
| | | |
Collapse
|
25
|
Xiong G, Wang SD, Niu Q, Wang Y, Xie XC, Tian DC, Wang XR. Possible existence of a band of extended states induced by inter-Landau-band mixing in a quantum Hall system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2006; 18:2029-2055. [PMID: 21697574 DOI: 10.1088/0953-8984/18/6/017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The mixing of states with opposite chiralities in a quantum Hall system is shown to have a delocalization effect. It is possible that extended states may form bands because of this mixing, as is shown through a numerical calculation on a two-channel network model. Based on this result, a new phase diagram with a narrow metallic phase separating two adjacent QH phases and/or separating a QH phase from the insulating phase is proposed. The data from recent non-scaling experiments are reanalysed and it is shown that they seem to be consistent with the new phase diagram. However, due to finite-size effects, further study on large system size is still needed to conclude whether there are extended state bands in the thermodynamic limit.
Collapse
Affiliation(s)
- Gang Xiong
- Physics Department, Beijing Normal University, Beijing 100875, People's Republic of China
| | | | | | | | | | | | | |
Collapse
|
26
|
Schweitzer L, Markos P. Universal conductance and conductivity at critical points in integer quantum Hall systems. PHYSICAL REVIEW LETTERS 2005; 95:256805. [PMID: 16384493 DOI: 10.1103/physrevlett.95.256805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2005] [Indexed: 05/05/2023]
Abstract
The sample averaged longitudinal two-terminal conductance and the respective Kubo conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, and , respectively. In the second-lowest Landau band, a critical conductance is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value . We argue that this difference is due to the multifractal structure of critical wave functions, a property that should generically show up in the conductance at quantum critical points.
Collapse
Affiliation(s)
- L Schweitzer
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | | |
Collapse
|
27
|
Pan W, Xia JS, Stormer HL, Tsui DC, Vicente CL, Adams ED, Sullivan NS, Pfeiffer LN, Baldwin KW, West KW. Quantization of the diagonal resistance: density gradients and the empirical resistance rule in a 2D system. PHYSICAL REVIEW LETTERS 2005; 95:066808. [PMID: 16090978 DOI: 10.1103/physrevlett.95.066808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2005] [Indexed: 05/03/2023]
Abstract
We have observed quantization of the diagonal resistance, R(xx), at the edges of several quantum Hall states. Each quantized R(xx) value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R(xy). Peaks in R(xx) occur at different positions in positive and negative magnetic fields. Practically all R(xx) features can be explained quantitatively by a 1%/cm electron density gradient. Therefore, R(xx) is determined by R(xy) and unrelated to the diagonal resistivity rho(xx). Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.
Collapse
Affiliation(s)
- W Pan
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | | | | | | | | | | | | | | | | | | |
Collapse
|
28
|
Li W, Csáthy GA, Tsui DC, Pfeiffer LN, West KW. Scaling and universality of integer quantum Hall plateau-to-plateau transitions. PHYSICAL REVIEW LETTERS 2005; 94:206807. [PMID: 16090272 DOI: 10.1103/physrevlett.94.206807] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2004] [Indexed: 05/03/2023]
Abstract
We have investigated the integer quantum Hall plateau-to-plateau transition in two-dimensional electrons confined to AlxGa(1-x)As-Al0.33Ga0.67As heterostructures over a broad range of Al concentration x. For x between 0.65% and 1.6%, where the dominant contribution to disorder is from the short-range alloy potential fluctuations, we observe a perfect power-law scaling in the temperature range from 30 mK to 1 K with a critical exponent kappa = 0.42 +/- 0.01.
Collapse
Affiliation(s)
- Wanli Li
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | | | | | | | | |
Collapse
|
29
|
Dubi Y, Meir Y, Avishai Y. Unifying model for several classes of two-dimensional phase transition. PHYSICAL REVIEW LETTERS 2005; 94:156406. [PMID: 15904168 DOI: 10.1103/physrevlett.94.156406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2004] [Indexed: 05/02/2023]
Abstract
A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator," classical percolation and, to some extent, superconductor-insulator transitions. Using real-space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed.
Collapse
Affiliation(s)
- Yonatan Dubi
- Physics Department, Ben-Gurion University, Beer Sheva 84105, Israel
| | | | | |
Collapse
|
30
|
Ilani S, Martin J, Teitelbaum E, Smet JH, Mahalu D, Umansky V, Yacoby A. The microscopic nature of localization in the quantum Hall effect. Nature 2004; 427:328-32. [PMID: 14737162 DOI: 10.1038/nature02230] [Citation(s) in RCA: 165] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2003] [Accepted: 11/21/2003] [Indexed: 11/09/2022]
Abstract
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties owing to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments on highly disordered samples have affirmed the validity of the single-particle picture, other experiments and some recent theories have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder.
Collapse
Affiliation(s)
- S Ilani
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
| | | | | | | | | | | | | |
Collapse
|
31
|
Peled E, Shahar D, Chen Y, Diez E, Sivco DL, Cho AY. Near-perfect correlation of the resistance components of mesoscopic samples at the quantum Hall regime. PHYSICAL REVIEW LETTERS 2003; 91:236802. [PMID: 14683205 DOI: 10.1103/physrevlett.91.236802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2003] [Indexed: 05/24/2023]
Abstract
We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=1 quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.
Collapse
Affiliation(s)
- E Peled
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | | | | | | | | | | |
Collapse
|
32
|
Kopelevich Y, Torres JHS, da Silva RR, Mrowka F, Kempa H, Esquinazi P. Reentrant metallic behavior of graphite in the quantum limit. PHYSICAL REVIEW LETTERS 2003; 90:156402. [PMID: 12732058 DOI: 10.1103/physrevlett.90.156402] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2002] [Indexed: 05/24/2023]
Abstract
Magnetotransport measurements performed on several well-characterized highly oriented pyrolitic graphite and single crystalline Kish graphite samples reveal a reentrant metallic behavior in the basal-plane resistance at high magnetic fields, when only the lowest Landau levels are occupied. The results suggest that the quantum Hall effect and Landau-level-quantization-induced superconducting correlations are relevant to understand the metalliclike state(s) in graphite in the quantum limit.
Collapse
Affiliation(s)
- Y Kopelevich
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil
| | | | | | | | | | | |
Collapse
|
33
|
Morgenstern M, Klijn J, Meyer C, Wiesendanger R. Real-space observation of drift States in a two-dimensional electron system at high magnetic fields. PHYSICAL REVIEW LETTERS 2003; 90:056804. [PMID: 12633386 DOI: 10.1103/physrevlett.90.056804] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2002] [Indexed: 05/24/2023]
Abstract
The local density of states of the adsorbate-induced two-dimensional electron system is studied in magnetic fields up to B=6 T. Landau quantization is observed and drift states with a width of about the magnetic length are found in agreement with theoretical predictions. At the tails of the Landau levels the states form closed paths indicating localization. These states show the expected energy dependence. A multifractal analysis applied to the data results in a nice parabolic shape of the characteristic f(alpha) spectra, but we find only a slight displacement of the origin from alpha=2.0 for the states in the center of the Landau level.
Collapse
Affiliation(s)
- M Morgenstern
- Institute of Applied Physics, Hamburg University, Jungiusstrasse 11, Germany
| | | | | | | |
Collapse
|
34
|
Hohls F, Zeitler U, Haug RJ, Meisels R, Dybko K, Kuchar F. Dynamical scaling of the quantum Hall plateau transition. PHYSICAL REVIEW LETTERS 2002; 89:276801. [PMID: 12513229 DOI: 10.1103/physrevlett.89.276801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2002] [Indexed: 05/24/2023]
Abstract
Using different experimental techniques, we examine the dynamical scaling of the quantum Hall plateau transition in a frequency range f=0.1-55 GHz. We present a scheme that allows for a simultaneous scaling analysis of these experiments and all other data in literature. We observe a universal scaling function with an exponent kappa=0.5+/-0.1, yielding a dynamical exponent z=0.9+/-0.2.
Collapse
Affiliation(s)
- F Hohls
- Institut für Festkörperphysik, Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany.
| | | | | | | | | | | |
Collapse
|
35
|
Avishai Y, Meir Y. New spin-orbit-induced universality class in the integer quantum Hall regime. PHYSICAL REVIEW LETTERS 2002; 89:076602. [PMID: 12190544 DOI: 10.1103/physrevlett.89.076602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2001] [Indexed: 05/23/2023]
Abstract
Using heuristic arguments and numerical simulations it is argued that the critical exponent nu describing the localization length divergence at the integer quantum-Hall transition is modified in the presence of spin-orbit scattering with short-range correlations. The exponent is very close to nu=4/3, the percolation correlation length exponent, consistent with the prediction of a semiclassical argument. In addition, a band of weakly localized states is conjectured.
Collapse
Affiliation(s)
- Yshai Avishai
- Department of Physics and Ilse Katz Center for Meso- and Nanoscale Science and Technology, Ben Gurion University, Beer Sheva, Israel
| | | |
Collapse
|
36
|
Hohls F, Zeitler U, Haug RJ. Hopping conductivity in the quantum Hall effect: revival of universal scaling. PHYSICAL REVIEW LETTERS 2002; 88:036802. [PMID: 11801077 DOI: 10.1103/physrevlett.88.036802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2001] [Indexed: 05/23/2023]
Abstract
We have measured the temperature dependence of the conductivity sigma(xx) of a two-dimensional electron system deep into the localized regime of the quantum Hall plateau transition. Using variable-range hopping theory we extract directly the localization length xi from this experiment. We use our results to study the scaling behavior of xi as a function of the filling factor distance /deltanu/ to the critical point of the transition. We find for all samples a power-law behavior xi equivalent to /deltanu/(-gamma) in agreement with the theoretically proposed universal exponent gamma = 2.35.
Collapse
Affiliation(s)
- F Hohls
- Institut für Festkörperphysik, Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany.
| | | | | |
Collapse
|
37
|
Xiong G, Wang SD, Niu Q, Tian DC, Wang XR. Metallic phase in quantum Hall systems due to inter-Landau-band mixing. PHYSICAL REVIEW LETTERS 2001; 87:216802. [PMID: 11736362 DOI: 10.1103/physrevlett.87.216802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2001] [Indexed: 05/23/2023]
Abstract
The electronic eigenstates of a quantum Hall (QH) system are chiral states. Strong inter-Landau-band mixings among these states can occur when the bandwidth is comparable to the spacing of two adjacent Landau bands. We show that mixing of localized states with opposite chirality can delocalize electronic states. Based on numerical results, we propose the existence of a metallic phase between two adjacent QH phases and between a QH phase and the insulating phase. This result is consistent with nonscaling behaviors observed in recent experiments on a quantum Hall liquid-to-insulator transition.
Collapse
Affiliation(s)
- G Xiong
- Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China
| | | | | | | | | |
Collapse
|
38
|
Moore JE, Zee A, Sinova J. Quantum hall plateau transition at order 1/N. PHYSICAL REVIEW LETTERS 2001; 87:046801. [PMID: 11461633 DOI: 10.1103/physrevlett.87.046801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2000] [Indexed: 05/23/2023]
Abstract
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law delocalization near the discrete extended-state energies E(n) = Planck's over 2piomega(c)(n+1 / 2), we study a generalization of the disorder-averaged Liouvillian framework for the lowest Landau level to N flavors of electron densities ( N = 1 for the physical case). We find analytically the large- N limit and 1/N corrections for all disorder strengths: at N = infinity this gives an estimate of the critical conductivity, and at order 1/N an estimate of the localization exponent nu.
Collapse
Affiliation(s)
- J E Moore
- Bell Labs, Lucent Technologies, 700 Mountain Avenue, Murray Hill, New Jersey 07974, USA
| | | | | |
Collapse
|
39
|
Eom J, Cho H, Kang W, Campman KL, Gossard AC, Bichler M, Wegscheider W. Quantum hall ferromagnetism in a two-dimensional electron system. Science 2000; 289:2320-3. [PMID: 11009411 DOI: 10.1126/science.289.5488.2320] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Experiments on a nearly spin degenerate two-dimensional electron system reveals unusual hysteretic and relaxational transport in the fractional quantum Hall effect regime. The transition between the spin-polarized (with fill fraction nu = 1/3) and spin-unpolarized (nu = 2/5) states is accompanied by a complicated series of hysteresis loops reminiscent of a classical ferromagnet. In correlation with the hysteresis, magnetoresistance can either grow or decay logarithmically in time with remarkable persistence and does not saturate. In contrast to the established models of relaxation, the relaxation rate exhibits an anomalous divergence as temperature is reduced. These results indicate the presence of novel two-dimensional ferromagnetism with a complicated magnetic domain dynamic.
Collapse
Affiliation(s)
- J Eom
- James Franck Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA. Department of Electrical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA. Walter Schottky Instit
| | | | | | | | | | | | | |
Collapse
|
40
|
Olsthoorn SM, Wei HP, Pruisken AM. Probing the plateau-insulator quantum phase transition in the quantum hall regime. PHYSICAL REVIEW LETTERS 2000; 84:1567-1570. [PMID: 11017569 DOI: 10.1103/physrevlett.84.1567] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/1998] [Indexed: 05/23/2023]
Abstract
We report quantum Hall experiments on the plateau-insulator transition in a low mobility In(0.53)Ga(0.47)As/InP heterostructure. The data for the longitudinal resistance rho(xx) follow an exponential law and we extract a critical exponent kappa = 0.55+/-0. 05 which is slightly different from the established value kappa = 0. 42+/-0.04 for the plateau transitions. Upon correction for inhomogeneity effects, which cause the critical conductance sigma(*)(xx) to depend marginally on temperature, our data indicate that the plateau-plateau and plateau-insulator transitions are in the same universality class.
Collapse
|
41
|
(Perturbed) Conformal Field Theory Applied to 2D Disordered Systems: An Introduction. ACTA ACUST UNITED AC 1997. [DOI: 10.1007/978-1-4899-1919-9_2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/08/2023]
|
42
|
Machida T, Hirai H, Komiyama S, Shiraki Y. Size-dependent transmission coefficients of edge channels in the quantum-Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16860-16863. [PMID: 9985815 DOI: 10.1103/physrevb.54.16860] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
43
|
Valfells S, Brooks JS, Wang Z, Takasaki S, Yamada J, Anzai H, Tokumoto M. Quantum Hall transitions in (TMTSF)2PF6. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16413-16416. [PMID: 9985757 DOI: 10.1103/physrevb.54.16413] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
44
|
Wang Z, Jovanovic B, Lee DH. Critical Conductance and Its Fluctuations at Integer Hall Plateau Transitions. PHYSICAL REVIEW LETTERS 1996; 77:4426-4429. [PMID: 10062535 DOI: 10.1103/physrevlett.77.4426] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
45
|
Wysokinski KI, Evers F, Brenig W. Classical analysis of a network model of quantum Hall systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:10720-10725. [PMID: 9984868 DOI: 10.1103/physrevb.54.10720] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
46
|
Sorensen ES, MacDonald AH. Integer quantum Hall effect in double-layer systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:10675-10687. [PMID: 9984864 DOI: 10.1103/physrevb.54.10675] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
47
|
Ho C, Chalker JT. Models for the integer quantum Hall effect: The network model, the Dirac equation, and a tight-binding Hamiltonian. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8708-8713. [PMID: 9984548 DOI: 10.1103/physrevb.54.8708] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
48
|
Pryadko LP, Zhang SC. Duality and universality for the Chern-Simons bosons. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:4953-4965. [PMID: 9986458 DOI: 10.1103/physrevb.54.4953] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
49
|
Lee DH, Wang Z. Effects of electron-electron interactions on the integer quantum Hall transitions. PHYSICAL REVIEW LETTERS 1996; 76:4014-4017. [PMID: 10061170 DOI: 10.1103/physrevlett.76.4014] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
50
|
Schultka N, Manousakis E. Three-dimensional x-y model with a Chern-Simons term. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:4782-4790. [PMID: 9984039 DOI: 10.1103/physrevb.53.4782] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|