First-Order Transitions in Weak Ising Spin-Orbit-Coupled Superconductors

TL;DR

This paper shows that weak Ising spin-orbit coupling in superconductors can lead to first-order phase transitions under large exchange fields, revealing new thermodynamic and spectroscopic features.

Contribution

It demonstrates the emergence of first-order transitions in weak-ISOC superconductors using free-energy analysis, contrasting with traditional gap-equation approaches.

Findings

First-order transitions occur in weak-ISOC superconductors at large exchange fields.

Two in-gap coherence peaks are identified as signatures of weak ISOC.

Conventional gap equations fail to determine the critical field in this regime.

Abstract

Ising spin-orbit coupling (ISOC) can strongly protect superconductivity against exchange-field-induced depairing, typically leading to critical fields far exceeding the Pauli limit and continuous (second-order) phase transitions. Here, using a free-energy approach, we demonstrate that first-order transitions can emerge in superconductors with weak ISOC under large exchange fields. In this regime, conventional theoretical approaches based on the gap equation fail to determine the thermodynamic critical field and instead yield only the supercooling field. Moreover, we identify two pronounced in-gap coherence peaks in the quasiparticle spectra, which represent the weak-ISOC manifestation of the previously reported mirage-gap states. Our results establish the importance of free-energy analysis in describing the first-order phase transitions in Ising superconductors and reveal distinct spectroscopic signatures of the weak-ISOC regime.