Observation of half-integer thermal Hall conductance

TL;DR

This paper reports the experimental measurement of fractional thermal Hall conductance in quantum Hall states, notably finding a fractional value of 2.5 times the fundamental unit for the =5/2 state, indicating non-abelian topological order.

Contribution

The study provides the first experimental evidence of fractional thermal Hall conductance in the =5/2 state, supporting its non-abelian topological nature.

Findings

Thermal Hall conductance of =5/2 state is 2.5 7 T, a fractional value.

Measurement confirms non-abelian topological order in the =5/2 state.

Thermal conductance quantization aligns with theoretical predictions for non-abelian states.

Abstract

Topological states of matter are characterized by topological invariant, which are physical quantities whose values are quantized and do not depend on details of the measured system. Of these, the easiest to probe in experiments is the electrical Hall conductance, which is expressed in units of $e^2/h$ ($e$ the electron charge, $h$ the Planck's constant). In the fractional quantum Hall effect (FQHE), fractional quantized values of the electrical Hall conductance attest to topologically ordered states, which are states that carry quasi particles with fractional charge and anyonic statistics. Another topological invariant, which is much harder to measure, is the thermal Hall conductance, expressed in units of $\kappa_0T=(\pi^2kB^2/3h)T$ ($kB$ the Boltzmann constant, $T$ the temperature). For the quantized thermal Hall conductance, a fractional value attests that the probed state of matter is non-abelian. Quasi particles in non-abelian states lead to a ground state degeneracy and perform topological unitary transformations among ground states when braided. As such, they may be useful for topological quantum computation. In this paper, we report our measurements of the thermal Hall conductance for several quantum Hall states in the first excited Landau level. Remarkably, we find the thermal Hall conductance of the $\nu=5/2$ state to be fractional, and to equal $2.5\kappa_0T$