Proposal for measuring the parity anomaly in a topological superconductor ring

TL;DR

This paper proposes an experimental method to detect the fundamental parity anomaly in topological superconductors by analyzing flux periodicity in a superconducting ring's conductance, linking it to topological invariants.

Contribution

It introduces a novel approach extending the Ambegaokar-Eckern-Schön formalism to relate thermodynamic and transport properties to the topological invariant, enabling definitive detection of the parity anomaly.

Findings

The flux periodicity of conductance reveals the fermion parity switch.

Topological conductance oscillations can be distinguished from non-topological ones.

Explicit relationships between charging energy, barrier transparency, and topological signatures are established.

Abstract

A topological superconductor ring is uniquely characterized by a switch in the ground state fermion number parity upon insertion of one superconducting flux quantum - a direct consequence of the topological `parity anomaly.' Despite the many other tantalizing signatures and applications of topological superconductors, this fundamental, defining property remains to be observed experimentally. Here we propose definitive detection of the fermion parity switch from the charging energy, temperature, and tunnel barrier dependence of the flux periodicity of two-terminal conductance of a floating superconductor ring. We extend the Ambegaokar-Eckern-Sch{\"o}n formalism for superconductors with a Coulomb charging energy to establish new explicit relationships between thermodynamic and transport properties of such a ring and the topological invariant of the superconductor. Crucially, we show that the topological contribution to the conductance oscillations can be isolated from Aharonov-Bohm oscillations of non-topological origin by their different dependence on the charging energy or barrier transparency.