Quantization of heat flow in the fractional quantum Hall regime

Quantum mechanics sets an upper bound on the amount of charge flow as well as on the amount of heat flow in ballistic onedimensional channels. The two relevant upper bounds, which combine only fundamental constants, are the quantum of the electrical conductance, G_e=e²/h, and the quantum of the thermal conductance, G_th=κ₀T=(π²k_B²/3h)T. Remarkably, the latter does not depend on the particles charge, particles exchange statistics, and is expected also to be insensitive to the interaction strength among the particles. However, unlike the  elative ease in observing the quantization of the electrical conductance, measuring accurately the thermal conductance is more challenging.

The universality of the G_th quantization in 1D ballistic channels was demonstrated for weakly interacting particles: phonons [1], photons [2], and in an electronic Fermi-liquid [3]. I will describe our recent experiments with heat flow in a strongly interacting system of 2D electrons in the fractional quantum Hall regime. In the lowest Landau level we studied particle-like states (v<½) and the more complex hole like states (½<v<1), which carry counter propagating neutral (zero net charge) modes [4]. We found quantization of G_th=κ0T in all these abelian states. In the first-excited Landau level (2<v<3), we concentrated on the even-denominator v=5/2 state, and found fractional quantization of the thermal conductance, G_th=½κ₀T, a definite mark of a non-abelian state harboring Majorana excitations [5].

1. K. Schwab, et al., Nature 404, 974 (2000)
2. M. Meschke, et al., Nature 444, 187 (2006)
3. S. Jezouin, et al., Science 342, 601 (2013)
4. M. Banerjee et. al., Nature 545, 75 (2017)
5. M. Banerjee et. al., arXiv: 1710.00492