Theory of Disorder-Induced Half-Integer Thermal Hall Conductance

TL;DR

This paper explains the observed half-integer thermal Hall conductance in disordered quantum Hall systems by proposing a model where disorder creates puddles with different conductance values, and interactions between them produce a macroscopic state with quantized 5/2 conductance.

Contribution

It introduces a disorder-based mechanism for the emergence of half-integer thermal Hall conductance, reconciling experimental results with theoretical predictions.

Findings

Disorder leads to puddles with local $rac{3}{2}$ or $rac{7}{2}$ conductance.

Interactions between puddles produce a coherent state with quantized $rac{5}{2}$ conductance.

Topological properties are determined by the macroscopic phase, not microscopic puddles.

Abstract

Electrons that are confined to a single Landau level in a two dimensional electron gas realize the effects of strong electron-electron repulsion in its purest form. The kinetic energy of individual electrons is completely quenched and all physical properties are dictated solely by many-body effects. A remarkable consequence is the emergence of new quasiparticles with fractional charge and exotic quantum statistics of which the most exciting ones are non-Abelian quasiparticles. A non-integer quantized thermal Hall conductance $\kappa_{xy}$ (in units of temperature times the universal constant $\pi^2 k_B^2 /3 h$; $h$ is the Planck constant and $k_B$ the Boltzmann constant) necessitates the existence of such quasiparticles. It has been predicted, and verified numerically, that such states are realized in the clean half-filled first Landau level of electrons with Coulomb repulsion, with $\kappa_{xy}$ being either $3/2$ or $7/2$. Excitingly, a recent experiment has indeed observed a half-integer value, which was measured, however, to be $\kappa_{xy}=5/2$. We resolve this contradiction within a picture where smooth disorder results in the formation of mesoscopic puddles with locally $\kappa_{xy}=3/2$ or $7/2$. Interactions between these puddles generate a coherent macroscopic state, which is reflected in an extended plateau with quantized $\kappa_{xy}=5/2$. The topological properties of quasiparticles at large distances are determined by the macroscopic phase, and not by the microscopic puddle where they reside. In principle, the same mechanism might also allow non-Abelian quasiparticles to emerge from a system comprised of microscopic Abelian puddles.