Observation of half-integer thermal Hall conductance

Understand

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).