Readout of parafermionic states by transport measurements

Ida E. Nielsen¹, Karsten Flensberg¹, Reinhold Egger², Michele Burrello^1*

¹Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
²Institute for theoretical physics, Heinrich Heine University, Duesseldorf, Germany

* Presenter:Michele Burrello, email:michele.burrello@nbi.ku.dk

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. In this talk, I will show that, for a pair of isolated parafermions, this nonlocal degree of freedom can be read by conductance measurements across standard metallic electrodes. I will discuss first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, the conductance reveals their shared fractional charge. I will 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.

Keywords: Parafermions, Quantum Hall effect, Superconductivity, Transport