Observation of half-integer thermal Hall conductance

Mitali Banerjee, Moty Heiblum (), Vladimir Umansky, Dima E. Feldman, Yuval Oreg and Ady Stern
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Mitali Banerjee: Weizmann Institute of Science
Moty Heiblum: Weizmann Institute of Science
Vladimir Umansky: Weizmann Institute of Science
Dima E. Feldman: Brown University
Yuval Oreg: Weizmann Institute of Science
Ady Stern: Weizmann Institute of Science

Nature, 2018, vol. 559, issue 7713, 205-210

Abstract: Abstract Topological states of matter are characterized by topological invariants, which are physical quantities whose values are quantized and do not depend on the details of the system (such as its shape, size and impurities). Of these quantities, the easiest to probe is the electrical Hall conductance, and fractional values (in units of e2/h, where e is the electronic charge and h is the Planck constant) of this quantity attest to topologically ordered states, which carry quasiparticles with fractional charge and anyonic statistics. Another topological invariant is the thermal Hall conductance, which is harder to measure. For the quantized thermal Hall conductance, a fractional value in units of κ0 (κ0 = π2kB2/(3h), where kB is the Boltzmann constant) proves that the state of matter is non-Abelian. Such non-Abelian states lead to ground-state degeneracy and perform topological unitary transformations when braided, which can be useful for topological quantum computation. Here we report measurements of the thermal Hall conductance of several quantum Hall states in the first excited Landau level and find that the thermal Hall conductance of the 5/2 state is compatible with a half-integer value of 2.5κ0, demonstrating its non-Abelian nature.

Date: 2018
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DOI: 10.1038/s41586-018-0184-1

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