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A method is proposed to extend the zero-temperature Hall-Klemm microscopictheory of the Knight shift $K$ in an anisotropic and correlated, multi-bandmetal to calculate $K(T)$ at finite temperatures $T$ both above and into itssuperconducting state. The transverse part of the magnetic induction ${\bfB}(t)={\bf B}_0+{\bf B}_1(t)$ causes adiabatic changes suitable for treatmentwith the Keldysh contour formalism and analytic continuation onto the realaxis. We propose that the Keldysh-modified version of the Gor'kov method can beused to evaluate $K(T)$ at high ${\bf B}_0$ both in the normal state, and byquantizing 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 beencalculated in detail, it appears that this approach could lead to the simpleresult $K_S(T)\approx a({\bf B}_0)-b({\bf B}_0)|\Delta({\bf B}_0,T)|^2$, 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 aidin the interpretation of experimental data on unconventional superconductors.

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