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

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 B ( t ) = B 0 + 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 B 0 both in the normal state, and by quantizing the conduction electrons or holes with Landau orbits arising from 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 ) ≈ a ( B 0 ) − b ( B 0 ) | Δ ( B 0 , T ) | 2 , where 2 | Δ ( 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.

Keywords

• Knight shift
• Type-II superconductor
• nuclear magnetic resonance
• anisotropy
• electron correlations