Competition between quantum-liquid and electron-solid phases in intermediate Landau levels

TL;DR

This paper investigates the competition between quantum-liquid and electron-solid phases in intermediate Landau levels, explaining observed reentrant quantum Hall effects through energy calculations of various phases.

Contribution

It provides a detailed energy comparison of phases in Landau levels n=1,2,3, revealing the conditions favoring electron solids or quantum liquids.

Findings

Quantum-liquid phases are stable near filling factors 1/(2s+1).

Electron solid phases (bubble phases) are favored between these fillings.

Reentrant integer quantum Hall effect explained by phase alternation.

Abstract

On the basis of energy calculations we investigate the competition between quantum-liquid and electron-solid phases in the Landau levels n=1,2, and 3 as a function of their partial filling factor. Whereas the quantum-liquid phases are stable only in the vicinity of quantized values 1/(2s+1) of the partial filling factor, an electron solid in the form of a triangular lattice of clusters with a few number of electrons (bubble phase) is energetically favorable between these fillings. This alternation of electron-solid phases, which are insulating because they are pinned by the residual impurities in the sample, and quantum liquids displaying the fractional quantum Hall effect explains a recently observed reentrance of the integral quantum Hall effect in the Landau levels n=1 and 2. Around half-filling of the last Landau level, a uni-directional charge density wave (stripe phase) has a lower energy than the bubble phase.