Interplay between fractional quantum Hall liquid and crystal phases at low filling
Abstract
The nature of the state at low Landau-level filling factors has been a long-standing puzzle in the field of the fractional quantum Hall effect (FQHE). While theoretical calculations suggest that a crystal is favored at filling factors $$\nu$$≲1/6, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $$\nu$$ 1/7, 2/11, 2/13, 3/19, 1/9, 2/15, and 2/17, which belong to the standard sequences $$\nu$$ =n/(6n ± 1) and $$\nu$$=n/(8n ± 1). To address this paradox, we investigate the nature of some of the low-$$\nu$$ states, specifically $$\nu$$= 1/7, 2/13, and 1/9, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. Finally, this suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.
- Authors:
-
[2];
[3];
[5];
[3]
- Pennsylvania State Univ., University Park, PA (United States); Henan Univ. of Science and Technology, Luoyang (China). Henan Key Lab. of Photoelectric Energy Storage Materials and Applications
- Inst. of Mathematical Sciences, HBNI, CIT Campus, Chennai (India)
- Pennsylvania State Univ., University Park, PA (United States)
- Univ. Paris-Saclay, Gif-sur-Yvette (France). Inst. de Physique Théorique
- Wrocław Univ. of Science and Technology, Wrocław (Poland)
- Publication Date:
- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Natural Science Foundation of China (NSFC)
- Contributing Org.:
- Penn State; Henan University of Science and Technology, China; Institute for Mathematical Sciences, India; CNRS France; Wroclaw University, Poland
- OSTI Identifier:
- 1773670
- Grant/Contract Number:
- SC0005042; 11604081; 11447008; 2014/14/A/ST3/00654
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Wigner crystal; fractional quantum Hall effect
Citation Formats
Zuo, Zheng-Wei, Balram, Ajit C., Pu, Songyang, Zhao, Jianyun, Jolicoeur, Thierry, Wójs, A., and Jain, J. K. Interplay between fractional quantum Hall liquid and crystal phases at low filling. United States: N. p., 2020.
Web. doi:10.1103/physrevb.102.075307.
Zuo, Zheng-Wei, Balram, Ajit C., Pu, Songyang, Zhao, Jianyun, Jolicoeur, Thierry, Wójs, A., & Jain, J. K. Interplay between fractional quantum Hall liquid and crystal phases at low filling. United States. https://doi.org/10.1103/physrevb.102.075307
Zuo, Zheng-Wei, Balram, Ajit C., Pu, Songyang, Zhao, Jianyun, Jolicoeur, Thierry, Wójs, A., and Jain, J. K. Wed .
"Interplay between fractional quantum Hall liquid and crystal phases at low filling". United States. https://doi.org/10.1103/physrevb.102.075307. https://www.osti.gov/servlets/purl/1773670.
@article{osti_1773670,
title = {Interplay between fractional quantum Hall liquid and crystal phases at low filling},
author = {Zuo, Zheng-Wei and Balram, Ajit C. and Pu, Songyang and Zhao, Jianyun and Jolicoeur, Thierry and Wójs, A. and Jain, J. K.},
abstractNote = {The nature of the state at low Landau-level filling factors has been a long-standing puzzle in the field of the fractional quantum Hall effect (FQHE). While theoretical calculations suggest that a crystal is favored at filling factors $\nu$≲1/6, experiments show, at somewhat elevated temperatures, minima in the longitudinal resistance that are associated with fractional quantum Hall effect at $\nu$ 1/7, 2/11, 2/13, 3/19, 1/9, 2/15, and 2/17, which belong to the standard sequences $\nu$ =n/(6n ± 1) and $\nu$=n/(8n ± 1). To address this paradox, we investigate the nature of some of the low-$\nu$ states, specifically $\nu$= 1/7, 2/13, and 1/9, by variational Monte Carlo, density matrix renormalization group, and exact diagonalization methods. We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. Finally, this suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced.},
doi = {10.1103/physrevb.102.075307},
journal = {Physical Review. B},
number = 7,
volume = 102,
place = {United States},
year = {Wed Aug 19 00:00:00 EDT 2020},
month = {Wed Aug 19 00:00:00 EDT 2020}
}
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