Interplay of Zeeman field, Rashba spin-orbit interaction, and superconductivity: Spin susceptibility

Abstract

We present a self-consistent theory to calculate the static and uniform spin susceptibility in superconductors under simultaneous Zeeman magnetic fields and Rashba-type spin-orbit coupling (SOC). Employing a single-band Bogoliubov-de Gennes Hamiltonian, we solve the gap equation for both conventional s-wave spin-singlet and six representative p-wave spin-triplet pairing states, categorized into opposite-spin-pairing (OSP) and equal-spin-pairing (ESP) classes. The Kubo formula, decomposed into intra- and interband particle-hole and particle-particle channels, provides two key constraints: At zero temperature, only particle-particle terms contribute, while at the critical temperature Tc, only particle-hole terms remain, ensuring χ(Tc−)=χN for continuous phase transitions. For s-wave pairing, a Zeeman field reduces Tc, whereas Rashba SOC preserves Tc but yields a residual zero temperature spin susceptibility χ(0) which approaches 2χN/3 in the strong SOC limit; combined fields create a Bogoliubov Fermi surface, resulting in a kink in χ(0). In contrast, p-wave states exhibit strong anisotropy: OSP states mimic spin-singlet pairing behavior for parallel Zeeman fields and ESP for transverse ones, while ESP states show the opposite, with Rashba SOC potentially changing the quasiparticle nodal structure, lowering Tc, or causing χzz(0) divergences. This framework offers quantitative benchmarks for Knight-shift experiments in non-centro-symmetric superconductors like A2Cr3As3 (A = Na, K, Rb, and Cs), enabling diagnostics to disentangle pairing symmetry, SOC strength, and Zeeman effects.

Source-reported materials — not catalogue approval

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