journal article·2021-03-03Open access

The quantum Hall effect in the absence of disorder

Kyung-Su Kim, Steven A. Kivelson

npj Quantum Materials· Volume 6· Issue 1

Abstract

Abstract It is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e., for the existence of “plateaus” in the quantum Hall effect. Here, we show that the existence of a quasi-particle Wigner crystal (QPWC) results in the persistence of plateaus of finite extent even in the limit of vanishing disorder. Several experimentally detectable features that characterize the behavior in the zero disorder limit are also explored.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Quantum and electron transport phenomena · Topological Materials and Phenomena · Advanced Physical and Chemical Molecular Interactions

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (33)

Show source-provided references
1. Chen, Y. et al. Microwave resonance of the 2D Wigner crystal around integer Landau fillings. Phys. Rev. Lett. 91, 016801 (2003).10.1103/PhysRevLett.91.016801 ↗
2. Lewis, R. M. et al. Wigner crystallization about ν = 3. Phys. E Low. Dimens. Syst. Nanostruct. 22, 104–107 (2004).10.1016/j.physe.2003.11.226 ↗
3. Moon, B.-H. et al. Microwave pinning modes near Landau filling ν = 1 in two-dimensional electron systems with alloy disorder. Phys. Rev. B 92, 035121 (2015).10.1103/PhysRevB.92.035121 ↗
4. Hatke, A. T. et al. Microwave spectroscopic observation of a Wigner solid within the ν = 1/2 fractional quantum Hall effect. Phys. Rev. B 95, 045417 (2017).10.1103/PhysRevB.95.045417 ↗
5. Han, Z. et al. Observation of a pinning mode in a Wigner solid with ν = 1/3 fractional quantum Hall excitations. Phys. Rev. Lett. 105, 126803 (2010).10.1103/PhysRevLett.105.167202 ↗
6. Girvin, S. M. The Quantum Hall Effect: Novel Excitations And Broken Symmetries. In Topological aspects of low dimensional systems (eds. Comtet, A., Jolicoeur, T., Ouvry, S. & David, F.) (Springer, 1999).
7. Girvin, S. M. & Yang, K. Modern Condensed Matter Physics (Cambridge Univ. Press, 2019).10.1017/9781316480649 ↗
8. Landau, L. D. & Lifshitz, E. M. Mechanics (Elsevier, 1988).
9. Laughlin, R. B. Quantized Hall conductivity in two dimensions. Phys. Rev. B 23, 5632–5633 (1981).10.1103/PhysRevB.23.5632 ↗
10. Tong, D. Lectures on the quantum Hall effect. Preprint at https://arxiv.org/abs/1606.06687 (2016).
11. Girvin, S. M. & Prange, R. The Quantum Hall Effect (Springer-Verlag, 1987).
12. Huckestein, B. Scaling theory of the integer quantum Hall effect. Rev. Mod. Phys. 67, 357–396 (1995).10.1103/RevModPhys.67.357 ↗
13. Grimes, C. C. & Adams, G. Evidence for a liquid-to-crystal phase transition in a classical, two-dimensional sheet of electrons. Phys. Rev. Lett. 42, 795–798 (1979).10.1103/PhysRevLett.42.795 ↗
14. Morf, R. H. Temperature dependence of the shear modulus and melting of the two-dimensional electron solid. Phys. Rev. Lett. 43, 931–935 (1979).10.1103/PhysRevLett.43.931 ↗
15. Chui, S. T. & Esfarjani, K. Finite-temperature two-dimensional Wigner transition. Phys. Rev. B 44, 11498–11501 (1991).10.1103/PhysRevB.44.11498 ↗
16. Fisher, D. S., Halperin, B. I. & Morf, R. Defects in the two-dimensional electron solid and implications for melting. Phys. Rev. B 20, 4692–4712 (1979).10.1103/PhysRevB.20.4692 ↗
17. Cockayne, E. & Elser, V. Energetics of point defects in the two-dimensional Wigner crystal. Phys. Rev. B 43, 623–629 (1991).10.1103/PhysRevB.43.623 ↗
18. Jain, J. K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989).10.1103/PhysRevLett.63.199 ↗
19. Lam, P. K. & Girvin, S. M. Liquid-solid transition and the fractional quantum-Hall effect. Phys. Rev. B 30, 473–475 (1984).10.1103/PhysRevB.30.473 ↗
20. Chitra, R., Giamarchi, T. & Le Doussal, P. Dynamical properties of the pinned Wigner crystal. Phys. Rev. Lett. 80, 3827–3830 (1998).10.1103/PhysRevLett.80.3827 ↗
21. Chitra, R., Giamarchi, T. & Le Doussal, P. Pinned Wigner crystals. Phys. Rev. B 65, 035312 (2001).10.1103/PhysRevB.65.035312 ↗
22. Fogler, M. M. & Huse, D. A. Dynamical response of a pinned two-dimensional Wigner crystal. Phys. Rev. B 62, 7553–7570 (2000).10.1103/PhysRevB.62.7553 ↗
23. Reichhardt, C. & Reichhardt, C. J. O. Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review. Rep. Prog. Phys. 80, 026501 (2016).10.1088/1361-6633/80/2/026501 ↗
24. Monarkha, Y. P. & Syvokon, V. E. A two-dimensional Wigner crystal. Low. Temp. Phys. 38, 1067–1095 (2012).10.1063/1.4770504 ↗
25. Fukuyama, H. & Lee, P. A. Dynamics of the charge-density wave. I. impurity pinning in a single chain. Phys. Rev. B 17, 535–541 (1978).10.1103/PhysRevB.17.535 ↗
26. Lee, P. A. & Fukuyama, H. Dynamics of the charge-density wave. II. long-range Coulomb effects in an array of chains. Phys. Rev. B 17, 542–548 (1978).10.1103/PhysRevB.17.542 ↗
27. Lee, P. A. & Rice, T. M. Electric field depinning of charge density waves. Phys. Rev. B 19, 3970–3980 (1979).10.1103/PhysRevB.19.3970 ↗
28. Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129–1181 (1988).10.1103/RevModPhys.60.1129 ↗
29. Fisher, D. S. Sliding charge-density waves as a dynamic critical phenomenon. Phys. Rev. B 31, 1396–1427 (1985).10.1103/PhysRevB.31.1396 ↗
30. Sneddon, L., Cross, M. C. & Fisher, D. S. Sliding conductivity of charge-density waves. Phys. Rev. Lett. 49, 292–295 (1982).10.1103/PhysRevLett.49.292 ↗
31. Imry, Y. & Ma, S. Random-field instability of the ordered state of continuous symmetry. Phys. Rev. Lett. 35, 1399–1401 (1975).10.1103/PhysRevLett.35.1399 ↗
32. Chung, Y. J. et al. Record-quality two-dimensional electron systems. Preprint at https://arxiv.org/abs/2010.02283 (2020).
33. Jiang, H. W. et al. Magnetotransport studies of the insulating phase around ν = 1/5 Landau-level filling. Phys. Rev. B 44, 8107–8114 (1991).10.1103/PhysRevB.44.8107 ↗