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

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 B(t) = B0 +B1(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 B0 both in the normal state, and by quantizing the conduction electrons or holes with Landau orbits arising from B0, 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 KS(T) ≈ a(B0) − b(B0)|∆(B0, T)|2, where 2|∆(B0, T)| is the effective superconducting gap. More generally, this approach can lead to analytic expressions for KS(T) for anisotropic, multiband Type-II superconductors of various orbital symmetries that could aid in the interpretation of experimental data on unconventional superconductors.