Contacts and Equilibration in the ν=5/2 Quantum Hall Effect

The thermal Hall conductance K_T of the fractional quantum Hall state at ν=5/2 has recently been measured to be K_T≈2.5(π²k_B²T/3h)[1]. The half-integer value of this result provides strong evidence for the presence of a Majorana edge mode and a corresponding quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether this measurement points to the realization of the PH-Pfaffian state or the anti-Pfaffian state has been the subject of debate [2][3]. Here we consider various edge-state scenarios which may explain the measured thermal conductance, paying close attention to the role of contacts and edge-state equilibration. Through a study of the kinetic equations describing the low-temperature transport in the anti-Pfaffian and PH Pfaffian edge states, we determine regimes of parameter space, controlling the interactions between the different edge modes, that agree with experiment. We also discuss how point-contact tunneling can distinguish various edge-state scenarios.

[1] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern. Nature, 559(7713):205–210, 2018.
[2] S. H. Simon. Phys. Rev. B, 97:121406, Mar 2018.
[3] D. E. Feldman. Phys. Rev. B, 98:167401, Oct 2018.