Nonanalytic features in response functions of anisotropic superconductors

Abstract

Nonanalytic features are interesting in physics as they carry valuable information about the physical properties of the system. In this work, we use a stationary-point analysis to deduce the nonanalytic features of dynamical correlation functions that are relevant to inelastic light scattering from superconductors with an anisotropic order parameter. We show that nodal regions of the order parameters are, quite generally, associated with linear-in-frequency scaling at low frequencies, the minima points of the order parameters are associated with step jumps, while the maxima points are associated with ln singularities. Despite this general association, we show that, depending on the anisotropy of the light-scattering vertex, these features can manifest themselves as various power laws, and even not remain singular at all. We are also able to demonstrate that the association of these nonanalytic features with the extrema and nodal points of the order parameter is, in fact, derived from a more universal behavior of functions near parabolic-like and saddle-like stationary points.

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