Broken rotation symmetry in the fractional quantum Hall system

TL;DR

This paper reveals that in strong magnetic fields, two-dimensional electron systems can form stable states that break rotational symmetry, resembling nematic liquid crystals, with implications for quantum Hall effects.

Contribution

It introduces the existence of rotational symmetry-breaking states in fractional quantum Hall systems, dependent on well thickness and electron density, and characterizes their symmetry properties.

Findings

Stable states break rotational symmetry but preserve translational symmetry.

The order parameter at 1/3 density resembles a nematic liquid crystal.

States with four- and six-fold axes exist at other filling factors.

Abstract

We demonstrate that the two-dimensonal electron system in a strong perpendicular magnetic field has stable states which break rotational but not translational symmetry. The Laughlin fluid becomes unstable to these states in quantum wells whose thickness exceeds a critical value which depends on the electron density. The order parameter at 1/3 reduced density resembles that of a nematic liquid crystal, in that a residual two-fold rotation axis is present in the low symmetry phase. At filling factors 1/5 and 1/7, there are states with four- and six-fold axes, as well. We discuss the experimental detection of these phases.