Anomalous Behavior of the Upper Critical Field in Extreme Type-II Superconductors at Low Temperatures

TL;DR

This paper investigates the unusual upward curvature of the upper critical magnetic field in extreme type-II superconductors at low temperatures, emphasizing the role of Landau quantization effects beyond standard theories.

Contribution

It introduces a numerical and analytical model that incorporates Landau level effects to explain the anomalous behavior of $H_{c2}(T)$ in extreme type-II superconductors.

Findings

Landau quantization causes upward curvature in $H_{c2}(T)$ at low temperatures.

The model explains the behavior for systems with high $H_{c2}$ slope at $T_{c0}$.

Quantitative agreement with numerical calculations is achieved.

Abstract

We present a detailed numerical calculation of the upper critical field $H_{c2}(T)$ for a bulk extreme type-II superconductor. Particular emphasis is placed on the high-field, low-temperature regime of the HT-phase diagram. In this regime it is necessary to go beyond the standard semi-classical theory and include the effects of Landau quantization of the electronic motion on the superconducting state. The presence of Landau level quantization induces an upward curvature in $H_{c2}(T)$ at $\sim 10%$ of $T_{c0}$ for those superconducting systems in which the slope of $H_{c2}(T)$ at $T_{c0}$ is $\geq $ 0.2 Tesla/Kelvin. We construct a simple analytical model that can account for this behavior based on the renormalization of the BCS coupling constant by the off-diagonal pairing of electrons on Landau levels.