Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling

TL;DR

This paper provides exact solutions for an electron pairing model incorporating spin-orbit interactions and Zeeman coupling, confirming the persistent p+ip-wave symmetry of the pairing order parameter across interaction strengths.

Contribution

It offers the first exact solutions for this class of models, validating mean field predictions and deriving analytical results for specific systems.

Findings

Pairing order parameter always has p+ip-wave symmetry

Exact solutions confirm mean field theory results

Analytical solutions for systems with spin-orbit and Zeeman interactions

Abstract

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing order parameter has always the $p+ip$-wave symmetry regardless of the strength of pairing interaction, justifying an important conclusion obtained by the mean field theory. Analytical results are derived for two simple systems with respectively spin-orbit interactions and Zeeman coupling.