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.
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We acknowledge B. Halperin and S. Simon for discussions. M.B. acknowledges the help and advice of Y. Gross regarding fabrication processes and R. Bhattacharyya for help with the cold amplifiers and Y. C. Chung and H. K. Choi for their help with the dilution refrigerator. M.H. acknowledges the continuous support of the Sub-Micron Center staff, and in particular Y. Rotblat, without whom this work would not be possible. M.H. acknowledges the support of the European Research Council under the European Community’s Seventh Framework Program (FP7/2007-2013)/ERC under grant agreement number 339070, the partial support of the Minerva foundation under grant number 711752, the Israeli Science Foundation ISF under grant number 459/16 and, together with V.U., the German Israeli Foundation (GIF) under grant number I-1241-303.10/2014. A.S and Y.O. acknowledge support from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013)/ERC Project MUNATOP, the DFG (CRC/Transregi 183, EI 519/7-1) and the Israel Science Foundation. Y.O. acknowledges the Binational Science Foundation (BSF). D.E.F.’s research was supported in part by the National Science Foundation under grant number DMR-1607451.
Nature thanks K. Shtengel, S. Simon and the other anonymous reviewer(s) for their contribution to the peer review of this work.