Signatures of topological phase transitions in Josephson current-phase discontinuities

TL;DR

This paper proposes a new method to detect topological phase transitions in superconducting nanostructures by observing Josephson current-phase discontinuities, which indicate zero-energy modes and fermion parity changes.

Contribution

It introduces an experimental approach based on Josephson current-phase relation discontinuities as signatures of topological phase transitions in finite-sized superconducting systems.

Findings

Discontinuities in the Josephson current-phase relation correspond to zero-energy modes.

Such discontinuities indicate a change in the fermion parity of the ground state.

The method can be experimentally detected through temperature dependence of the current.

Abstract

Topological superconductors differ from topologically trivial ones for the presence of topologically protected zero-energy modes. To date, experimental evidence of topological superconductivity in nanostructures has been mainly obtained by measuring the zero-bias conductance peak via tunneling spectroscopy. Here, we propose an alternative and complementary experimental recipe to detect topological phase transitions in these systems. We show in fact that, for a finite-sized system with broken time-reversal symmetry, discontinuities in the Josephson current-phase relation correspond to the presence of zero-energy modes and to a change in the fermion parity of the groundstate. Such discontinuities can be experimentally revealed by a characteristic temperature dependence of the current, and can be related to a finite anomalous current at zero phase in systems with broken phase-inversion symmetry.