Readout of parafermionic states by transport measurements

Ida E. Nielsen, Karsten Flensberg, Reinhold Egger, Michele Burrello

Published 2021-09-06Version 1

Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, nonabelian anyons which share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this nonlocal degree of freedom can be read by conductance measurements across standard metallic electrodes. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, the conductance reveals their shared fractional charge. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor. Depending on the induced pairing, parafermion overlap, and charging energy, such a device displays different patterns as a function of its induced charge. The zero-bias conductance allows us to distinguish a strongly-blockaded quantum dot regime, an intermediate pairing regime with a sixfold pattern of peaks repeating with periodicity $2e$, and a deep topological regime characterized by an $e/3$ periodicity.