Superconducting Upper Critical Field Near a 2D Van Hove Singularity

TL;DR

This paper calculates the upper critical magnetic field in a 2D superconductor near a van-Hove singularity, revealing a strong enhancement at weak coupling and a novel scaling relation, linked to non-Fermi liquid behavior.

Contribution

It introduces a theoretical analysis of $H_{c2}(T)$ near a van-Hove singularity, showing a new scaling law and connecting it to non-Fermi liquid decay of correlations.

Findings

Zero temperature $H_{c2}$ is strongly enhanced at weak coupling.

Scaling of $H_{c2}(0)$ with $T_c$ is proportional to $T_c^{\sqrt{2}}$.

Normal state pair correlations decay non-Fermi liquid style near van-Hove points.

Abstract

The superconducting upper critical field $H_{c2}(T)$ of a two dimensional BCS superconductor is calculated in the vicinity of a van-Hove singularity. The zero temperature upper critical field is strongly enhanced at weak coupling when the Fermi contour coincides with van-Hove points, scaling as $H_{c2}(0) \propto T_c^{\sqrt{2}}$ compared to the usual result $H_{c2}(0) \propto T_c^{2}$. The result can be interpreted in terms of the non-Fermi liquid decay of normal state pair correlations in the vicinity of a van-Hove point.