Observation of half-integer thermal Hall conductance

Quantum mechanics sets an upper bound on the amount of charge flow as well as on the amount of heat flow in ballistic one-dimensional channels. The two relevant upper bounds, that combine only fundamental constants, are the quantum of the electrical conductance, G_e=η e²/h with η =e*/e and the quantum of the thermal conductance, G_th=k₀T=(π²k_B²/3h)T [1]. Remarkably, the latter does not depend on particles charge; particles statistics; and even the interaction strength among the particles [2].
Unlike the relative ease in determining accurately the quantization of the electrical conductance, measuring accurately the thermal conductance is more challenging as heat flow is not conserved, accurate and noninvasive temperature measurements not trivial, and inter-mode equilibration is not fully understood.
The universality of the quantum of G_th was already demonstrated for weakly interacting particles: phonons [3], photons [4], and electronic Fermi-liquids [5]. I will describe our work on thermal conductance measurements in the QHE regime. We first focused on the Integer, Laughlin’s, and hole-conjugate (½< filling <1) states [6] - proving the universality of k₀. We extended our studies to the fractional states in the first-excited Landau level (2<v<3), and in particular on the v=5/2 state. We find in the latter a deviation from the quantization of the thermal conductance, agreeing in good accuracy with G_th=(2+½)k₀T; suggesting the non-abelian character of the state [7]. This topological order was not expected in previous numerical works.
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2. C. L. Kane et al., Phys. Rev. B 55, 15832 (1997)
3. K. Schwab et al., Nature 404, 974 (2000)
4. M. Meschke et al., Nature 444, 187 (2006)
5. S. Jezouin et al., Science 342, 601 (2013)
6. M. Banerjee et. al., Nature 545, 75 (2017)
7. M. Banerjee et. al., Nature 559, 205 (2018)