Towards a Microscopic Theory of the Knight Shift in an Anisotropic, Multiband Type-II Superconductor

TL;DR

This paper proposes a microscopic method to calculate the temperature-dependent Knight shift in anisotropic, multiband Type-II superconductors, extending existing theories to finite temperatures and magnetic fields.

Contribution

It introduces a Keldysh-modified Gor'kov approach for evaluating the Knight shift in complex superconductors at finite temperatures and high magnetic fields.

Findings

Potential to derive simple formulas for Knight shift in superconductors.

Framework applicable to various orbital symmetries and experimental interpretations.

Extension of microscopic theory to finite temperature and magnetic field regimes.

Abstract

A method is proposed to extend the zero-temperature Hall-Klemm microscopic theory of the Knight shift $K$ in an anisotropic and correlated, multi-band metal to calculate $K(T)$ at finite temperatures $T$ both above and into its superconducting state. The transverse part of the magnetic induction ${\bf B}(t)={\bf B}_0+{\bf B}_1(t)$ causes adiabatic changes suitable for treatment with the Keldysh contour formalism and analytic continuation onto the real axis. We propose that the Keldysh-modified version of the Gor'kov method can be used to evaluate $K(T)$ at high ${\bf B}_0$ both in the normal state, and by quantizing the conduction electrons or holes with Landau orbits arising from ${\bf B}_0$, also in the entire superconducting regime for an anisotropic, multiband Type-II BCS superconductor. Although the details have not yet been calculated in detail, it appears that this approach could lead to the simple result $K_S(T)\approx a({\bf B}_0)-b({\bf B}_0)|\Delta({\bf B}_0,T)|^2$, where $2|\Delta({\bf B}_0,T)|$ is the effective superconducting gap. More generally, this approach can lead to analytic expressions for $K_S(T)$ for anisotropic, multiband Type-II superconductors of various orbital symmetries that could aid in the interpretation of experimental data on unconventional superconductors.