Spatially Ordered Fractional Quantum Hall States

TL;DR

This paper explores various spatially ordered phases in fractional quantum Hall liquids, deriving their properties and phase transitions using a Chern--Simons Landau--Ginzburg framework, including effects of substrate coupling.

Contribution

It introduces a theoretical framework to describe spatially ordered fractional quantum Hall states and analyzes their phase transitions and substrate effects.

Findings

Derived long-wavelength properties of Hall hexatic, smectic, and crystal phases.

Mapped these phases to spatially ordered superfluids using Chern--Simons theory.

Discussed influence of periodic and anisotropic substrates on these states.

Abstract

Fractional quantum Hall liquids can accomodate various degrees of spatial ordering. The most likely scenarios are a Hall hexatic, Hall smectic, and Hall crystal, in which respectively orientational, one--dimensional translational, and two--dimensional translational symmetries are broken. I derive the long--wavelength properties of these phases and the transitions between them using the Chern--Simons Landau--Ginzburg mapping, which relates them to spatially ordered superfluids. The effects of coupling to a periodic or anisotropic ``substrate'' (e.g. a gate array) are also discussed.