Signatures of Topological Transitions in the Spin Susceptibility of Josephson Junctions

TL;DR

This paper theoretically demonstrates that the spin susceptibility in planar Josephson junctions exhibits distinct signatures, such as sharp peaks, during topological transitions, providing a measurable way to detect topological superconducting states.

Contribution

It introduces the use of spin susceptibility as a robust fingerprint for topological transitions in Josephson junctions, supported by analytical and numerical models.

Findings

Sharp peaks in spin susceptibility indicate topological transitions.

Spin susceptibility signatures are robust even with narrow superconducting leads.

The amplitude of spin susceptibility reveals information about the topological gap.

Abstract

We theoretically investigate how the spin susceptibility of a planar Josephson junction is affected when the system transits into the topological superconducting state. We show that the magnetic flux and magnetic field dependence of the spin susceptibility closely maps the phase diagram of the system. In the absence of an external magnetic flux the system can self-tune into the topological superconducting state by minimizing its free energy. Self-tuned topological transitions are accompanied by sharp peaks in the spin susceptibility, which can therefore be use as measurable fingerprints for detecting the topological superconducting state. Away from the peaks, the amplitude of the spin susceptibility can provide qualitative information about the relative size of the topological gap. The signatures in the spin susceptibility are robust, even in junctions with narrow superconducting leads, where critical current minima may no longer serve as an indication of topological phase transitions. Numerical simulations are complemented with simplified analytical models capable of capturing the main features predicted for the spin susceptibility behavior. The predicted results could be particularly relevant for future experiments on realization and detection of the topological superconducting state in planar Josephson junctions.