Charge density waves and their transitions in anisotropic quantum Hall systems

Yuchi He,Kang Yang,Roger S K Mong,Mark Oliver Goerbig

doi:10.1038/s42005-021-00613-4

Abstract

In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the N = 2 Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the 2-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the 2-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.

Highlights

In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions
We provide a quantitative comparison between analytical HF and numerical density matrix renormalization group (DMRG) calculations to study the charge density wave (CDW) phases of spin-polarised electrons in the N = 2 LL under a mass anisotropy, which can be realised in a 2D electron gas in AlAs quantum wells with a mass anisotropy mx/my ≈ 541
We indicate the regime of the stripe crystal computed from refs. 45,47,49, in which it is believed that the unidirectional stripe phase computed here should correspond to the stripe crystal[25]

Summary

Introduction

External anisotropy has been a useful tool to tune different phases and study their competitions. It is interesting to investigate how different QH phases, e.g., gapped QH fluid[12,13,14,15,16,17,18,19] or gapless composite fermion liquid states[20,21,22,23], can be tuned through external anisotropy. These studies greatly enhance the understanding of topological robustness against geometric perturbation. We can use both theoretical and numerical calculations to study how higher-LL QH systems react to anisotropy

Methods

Results

Conclusion