Kavli Affiliate: Yi Zhou
| First 5 Authors: Chen Pang, Yi Zhou, , ,
| Summary:
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 $T_c$, only particle-hole terms remain, ensuring $chi(T_c^{-}) =
chi_N$ for continuous phase transitions. For $s$-wave pairing, a Zeeman field
reduces $T_c$, whereas Rashba SOC preserves $T_c$ but yields a residual zero
temperature spin susceptibility $chi(0)$ which approaches $2chi_N/3$ in the
strong SOC limit; combined fields create a Bogoliubov Fermi surface, resulting
in a kink in $chi(0)$. 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 $T_c$, or
causing $chi_{zz}(0)$ divergences. This framework offers quantitative
benchmarks for Knight-shift experiments in non-centrosymmetric superconductors
like A$_2$Cr$_3$As$_3$ (A = Na, K, Rb, and Cs), enabling diagnostics to
disentangle pairing symmetry, SOC strength, and Zeeman effects.
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