Microscopic model of the Knight shift in an anisotropic type-II superconductor

We have simplified our model of the Knight shift in an anisotropic metal and superconductor by forcing the Hamiltonian for an electron in the Landau orbits for an ellipsoidally anisotropic single electron Hamiltonian and the Zeeman interaction to be relativistically consistent. The resulting Hamiltonian with three effective masses in the three directions of an orthorhombic crystal is invariant under the most general proper Lorentz transformation involving general rotations about all three crystal axes and general boosts in all three directions. The non-relativistic limit then has the following general properties: there is no Zeeman interaction for a one-dimensional metal, and for a two-dimensional metal, the Zeeman interaction is only present for the magnetic field applied perpendicular to the conducting plane. These exact results show that for the field parallel to the layers of a highly layered superconductor or for any field direction in a quasi-one-dimensional superconductor, the temperature dependence of the Knight shift in the superconducting state should either vanish or be very weak. Hence, many Knight shift measurements on such superconducting materials, while correct, have been misinterpreted in the literature.