Analytic Density of States in the Abrikosov-Gorkov Theory

TL;DR

This paper presents an exact analytic solution for the density of states in superconductors with paramagnetic impurities within the Abrikosov-Gorkov theory, enhancing both fundamental understanding and computational efficiency.

Contribution

It introduces a precise analytic expression for the density of states across all regimes of the Abrikosov-Gorkov theory, replacing previous approximate numerical solutions.

Findings

Exact analytic density of states derived

Solution valid for both gapped and gapless regimes

Facilitates improved calculations of tunneling conductances

Abstract

Since the early 1960s, Abrikosov-Gorkov theory has been used to describe superconductors with paramagnetic impurities. Interestingly, the density of states resulting from the theoretical framework has to date only been known approximately, as a numeric solution of a complex polynomial. Here we introduce an exact analytic solution for the density of states of a superconductor with paramagnetic impurities. The solution is valid in the whole regime of Abrikosov-Gorkov theory; both where there is an energy gap and gapless. While of fundamental interest, we argue that this solution also has computational benefits in the evaluation of integrals for tunneling conductances and allows for an analytic description of materials with densities of states that are modeled from the basic Abrikosov-Gorkov density of states.