1
|
Zhao PL, Lu HZ, Xie XC. Theory for Magnetic-Field-Driven 3D Metal-Insulator Transitions in the Quantum Limit. PHYSICAL REVIEW LETTERS 2021; 127:046602. [PMID: 34355953 DOI: 10.1103/physrevlett.127.046602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Revised: 04/07/2021] [Accepted: 06/17/2021] [Indexed: 06/13/2023]
Abstract
Metal-insulator transitions driven by magnetic fields have been extensively studied in 2D, but a 3D theory is still lacking. Motivated by recent experiments, we develop a scaling theory for the metal-insulator transitions in the strong-magnetic-field quantum limit of a 3D system. By using a renormalization-group calculation to treat electron-electron interactions, electron-phonon interactions, and disorder on the same footing, we obtain the critical exponent that characterizes the scaling relations of the resistivity to temperature and magnetic field. By comparing the critical exponent with those in a recent experiment [F. Tang et al., Nature (London) 569, 537 (2019)NATUAS0028-083610.1038/s41586-019-1180-9], we conclude that the insulating ground state was not only a charge-density wave driven by electron-phonon interactions but also coexisting with strong electron-electron interactions and backscattering disorder. We also propose a current-scaling experiment for further verification. Our theory will be helpful for exploring the emergent territory of 3D metal-insulator transitions under strong magnetic fields.
Collapse
Affiliation(s)
- Peng-Lu Zhao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, West Building 3, No. 10, Xibeiwang East Road, Haidian District, Beijing 100193, China
| |
Collapse
|
2
|
Fox EJ, Rosen IT, Yang Y, Jones GR, Elmquist RE, Kou X, Pan L, Wang KL, Goldhaber-Gordon D. Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect. PHYSICAL REVIEW. B 2018; 98:10.1103/PhysRevB.98.075145. [PMID: 30984899 PMCID: PMC6459416 DOI: 10.1103/physrevb.98.075145] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating two-dimensional bulk, without requiring an external magnetic field. Here, we explore the potential of this effect in magnetic topological insulator thin films for metrological applications. Using a cryogenic current comparator system, we measure quantization of the Hall resistance to within one part per million and, at lower current bias, longitudinal resistivity under 10 mΩ at zero magnetic field. Increasing the current density past a critical value leads to a breakdown of the quantized, low-dissipation state, which we attribute to electron heating in bulk current flow. We further investigate the prebreakdown regime by measuring transport dependence on temperature, current, and geometry, and find evidence for bulk dissipation, including thermal activation and possible variable-range hopping.
Collapse
Affiliation(s)
- E. J. Fox
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
| | - I. T. Rosen
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Yanfei Yang
- National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899-8171, USA
| | - George R. Jones
- National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899-8171, USA
| | - Randolph E. Elmquist
- National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899-8171, USA
| | - Xufeng Kou
- Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
- School of Information Science and Technology, ShanghaiTech University 201210, China
| | - Lei Pan
- Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Kang L. Wang
- Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - D. Goldhaber-Gordon
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
| |
Collapse
|
3
|
Stier AV, Ellis CT, Kwon J, Xing H, Zhang H, Eason D, Strasser G, Morimoto T, Aoki H, Zeng H, McCombe BD, Cerne J. Terahertz Dynamics of a Topologically Protected State: Quantum Hall Effect Plateaus near the Cyclotron Resonance of a Two-Dimensional Electron Gas. PHYSICAL REVIEW LETTERS 2015; 115:247401. [PMID: 26705653 DOI: 10.1103/physrevlett.115.247401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2015] [Indexed: 06/05/2023]
Abstract
We measure the Hall conductivity of a two-dimensional electron gas formed at a GaAs/AlGaAs heterojunction in the terahertz regime close to the cyclotron resonance frequency using highly sensitive Faraday rotation measurements. The sample is electrically gated, allowing the electron density to be changed continuously by more than a factor of 3. We observe clear plateaulike and steplike features in the Faraday rotation angle vs electron density and magnetic field (Landau-level filling factor) even at fields or frequencies very close to cyclotron resonance absorption. These features are the high frequency manifestation of quantum Hall plateaus-a signature of topologically protected edge states. We observe both odd and even filling factor plateaus and explore the temperature dependence of these plateaus. Although dynamical scaling theory begins to break down in the frequency region of our measurements, we find good agreement with theory.
Collapse
Affiliation(s)
- A V Stier
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - C T Ellis
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - J Kwon
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - H Xing
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - H Zhang
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - D Eason
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - G Strasser
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - T Morimoto
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - H Aoki
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - H Zeng
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - B D McCombe
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| | - J Cerne
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
| |
Collapse
|
4
|
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
|
5
|
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
|
6
|
KALUGIN NG, SAĞOL BE, STELLMACH C, BUß A, HIRSCH A, NACHTWEI G, HEIN G. RELAXATION OSCILLATIONS AND DYNAMICAL PROPERTIES OF A BISTABLE QUANTUM HALL SYSTEM. INTERNATIONAL JOURNAL OF NANOSCIENCE 2003. [DOI: 10.1142/s0219581x0300167x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We present a simple relaxation oscillator based on a quantum Hall device with Corbino geometry near the breakdown of the quantum Hall effect. The amplitude of the observed relaxation oscillations is found many times bigger than one can expect from the hysteresis of the quantum Hall effect breakdown, measured at constant currents. This result is explained by a dynamical suppression of hopping contribution to the conductivity σxx, and corresponding dynamical reduction of localization length ξ.
Collapse
Affiliation(s)
- N. G. KALUGIN
- Institut für Technische Physik, TU-Braunschweig, D-38106 Braunschweig, Germany
- Department of Physics, Texas A&M University, College Station, TX 77843-4242, USA
| | - B. E. SAĞOL
- Institut für Technische Physik, TU-Braunschweig, D-38106 Braunschweig, Germany
| | - C. STELLMACH
- Institut für Technische Physik, TU-Braunschweig, D-38106 Braunschweig, Germany
| | - A. BUß
- Institut für Technische Physik, TU-Braunschweig, D-38106 Braunschweig, Germany
| | - A. HIRSCH
- Institut für Technische Physik, TU-Braunschweig, D-38106 Braunschweig, Germany
| | - G. NACHTWEI
- Institut für Technische Physik, TU-Braunschweig, D-38106 Braunschweig, Germany
| | - G. HEIN
- Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Germany
| |
Collapse
|
7
|
Yang CL, Zudov MA, Knuuttila TA, Du RR, Pfeiffer LN, West KW. Observation of microwave-induced zero-conductance state in Corbino rings of a two-dimensional electron system. PHYSICAL REVIEW LETTERS 2003; 91:096803. [PMID: 14525201 DOI: 10.1103/physrevlett.91.096803] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2003] [Indexed: 05/24/2023]
Abstract
Using Corbino samples we have observed oscillatory dc conductance in a high-mobility two-dimensional electron system when it is subjected to crossed microwave and magnetic fields. At the strongest of the oscillation minima the conductance is found to be vanishingly small, indicating a macroscopic insulating state associated with this minimum. With increasing voltage bias, a crossover from Ohmic to electron-heating regime is observed.
Collapse
Affiliation(s)
- C L Yang
- Department of Physics, University of Utah, Salt Lake City, UT 84112, USA
| | | | | | | | | | | |
Collapse
|
8
|
Chen Y, Lewis RM, Engel LW, Tsui DC, Ye PD, Pfeiffer LN, West KW. Microwave resonance of the 2D Wigner crystal around integer Landau fillings. PHYSICAL REVIEW LETTERS 2003; 91:016801. [PMID: 12906562 DOI: 10.1103/physrevlett.91.016801] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2003] [Indexed: 05/24/2023]
Abstract
We have observed a resonance in the real part of the finite frequency diagonal conductivity using microwave absorption measurements in high quality 2D electron systems near integer fillings. The resonance exists in some neighborhood of filling factor around corresponding integers and is qualitatively similar to previously observed resonance of weakly pinned Wigner crystal in high B and very small filling factor regime. Data measured around both nu=1 and nu=2 are presented. We interpret the resonance as the signature of the Wigner crystal state around integer Landau levels.
Collapse
Affiliation(s)
- Yong Chen
- National High Magnetic Field Laboratory, 1800 E. Paul Dirac Drive, Tallahassee, Florida 32310, USA
| | | | | | | | | | | | | |
Collapse
|
9
|
Possanzini C, Fletcher R, Coleridge PT, Feng Y, Williams RL, Maan JC. Diffusion thermopower of a two-dimensional hole gas in SiGe in a quantum Hall insulating state. PHYSICAL REVIEW LETTERS 2003; 90:176601. [PMID: 12786087 DOI: 10.1103/physrevlett.90.176601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2002] [Indexed: 05/24/2023]
Abstract
Both the temperature dependence of resistivity and thermopower of a two-dimensional hole gas in SiGe show a reentrant metal-insulator transition at filling factor nu=1.5, but with strikingly different behavior of the two coefficients. As the temperature is decreased in the insulating state, the resistivity diverges exponentially while the thermopower decreases rapidly, suggesting that the insulating state is due to the presence of a mobility edge rather than a gap at the Fermi energy.
Collapse
Affiliation(s)
- C Possanzini
- Research Institute for Materials, High Field Magnet Laboratory, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands
| | | | | | | | | | | |
Collapse
|
10
|
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
|
11
|
Shashkin AA, Kravchenko SV, Klapwijk TM. Metal-insulator transition in a 2D electron gas: equivalence of two approaches for determining the critical point. PHYSICAL REVIEW LETTERS 2001; 87:266402. [PMID: 11800848 DOI: 10.1103/physrevlett.87.266402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2001] [Indexed: 05/23/2023]
Abstract
The critical electron density for the metal-insulator transition in a two-dimensional electron gas can be determined by two distinct methods: (i) a sign change of the temperature derivative of the resistance, and (ii) vanishing activation energy and vanishing nonlinearity of current-voltage characteristics as extrapolated from the insulating side. We find that, in zero magnetic field (but not in the presence of a parallel magnetic field), both methods give equivalent results, adding support to the existence of a true zero-field metal-insulator transition.
Collapse
Affiliation(s)
- A A Shashkin
- Physics Department, Northeastern University, Boston, Massachusetts 02115, USA
| | | | | |
Collapse
|
12
|
Hohls F, Zeitler U, Haug RJ. High frequency conductivity in the quantum hall regime. PHYSICAL REVIEW LETTERS 2001; 86:5124-5127. [PMID: 11384437 DOI: 10.1103/physrevlett.86.5124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2000] [Indexed: 05/23/2023]
Abstract
We have measured the complex conductivity sigma(xx) of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that sigma(xx) can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length xi. Even for large filling factor distances deltanu from the critical point we find xi approximately equals deltanu(-gamma) with a scaling exponent gamma = 2.3.
Collapse
Affiliation(s)
- F Hohls
- Institut für Festkörperphysik, Universität Hannover, Applestrasse 2, 30167 Hannover, Germany.
| | | | | |
Collapse
|
13
|
Kravchenko SV, Simonian D, Sarachik MP, Mason W, Furneaux JE. Electric Field Scaling at a B=0 Metal-Insulator Transition in Two Dimensions. PHYSICAL REVIEW LETTERS 1996; 77:4938-4941. [PMID: 10062672 DOI: 10.1103/physrevlett.77.4938] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
14
|
Polyakov DG. Spin-flip scattering in the quantum Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:15777-15788. [PMID: 9983414 DOI: 10.1103/physrevb.53.15777] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
15
|
Shahbazyan TV, Raikh ME. Surface plasmon in a two-dimensional Anderson insulator with interactions. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:7299-7307. [PMID: 9982177 DOI: 10.1103/physrevb.53.7299] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
16
|
Fogler MM, Shklovskii BI. Collapse of spin splitting in the quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:17366-17378. [PMID: 9981166 DOI: 10.1103/physrevb.52.17366] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
17
|
Glozman I, Johnson CE, Jiang HW. Path-dependent conductivity in the regime of floating delocalized states. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:14348-14351. [PMID: 9980756 DOI: 10.1103/physrevb.52.r14348] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
18
|
Hanna CB, Arovas DP, Mullen K, Girvin SM. Effect of spin degeneracy on scaling in the quantum Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:5221-5232. [PMID: 9981707 DOI: 10.1103/physrevb.52.5221] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
19
|
Bleibaum O, Böttger H, Bryksin VV, Schulz F. Hopping transport in a magnetic field: Kadanoff-Baym-Keldysh approach and magnetoconductivity. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:14020-14034. [PMID: 9978327 DOI: 10.1103/physrevb.51.14020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
20
|
Kravchenko SV, Mason WE, Bowker GE, Furneaux JE, Pudalov VM, D'Iorio M. Scaling of an anomalous metal-insulator transition in a two-dimensional system in silicon at B=0. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:7038-7045. [PMID: 9977262 DOI: 10.1103/physrevb.51.7038] [Citation(s) in RCA: 215] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
21
|
Polyakov DG, Shklovskii BI. Activated conductivity in the quantum Hall effect. PHYSICAL REVIEW LETTERS 1994; 73:1150-1153. [PMID: 10057637 DOI: 10.1103/physrevlett.73.1150] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
22
|
Aleiner IL, Shklovskii BI. Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:13721-13727. [PMID: 10010316 DOI: 10.1103/physrevb.49.13721] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|