Readout of parafermionic states by transport measurements

TL;DR

This paper proposes methods to detect parafermionic states in fractional quantum Hall systems using conductance measurements, revealing their fractional charge and nonlocal properties through specific transport signatures.

Contribution

It introduces two experimental setups for reading out parafermionic states via transport measurements, advancing detection techniques in topological quantum systems.

Findings

Conductance peaks reveal shared fractional charge of parafermions.

Zero-bias peaks exhibit $e/3$ periodicity indicating parafermionic modes.

Transport signatures distinguish topological parafermionic states from trivial states.

Abstract

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, non-Abelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the low-energy limit, its conductance peaks reveal their shared fractional charge yielding a three-state telegraph noise for weak quasiparticle poisoning. We then examine the two-terminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic $e/3$ periodicity of its zero-bias peaks in the deep topological regime, thus signalling the presence of parafermionic modes.