Upper magnetic field in superconducting Dirac semi-metal

TL;DR

This paper investigates the temperature dependence of the upper critical magnetic field in superconducting Dirac semi-metals, revealing deviations from conventional behavior and establishing a universal reduced field ratio consistent with experimental data.

Contribution

It introduces a semi-classical model for $H_{c2}$ in Dirac semi-metals, showing universal reduced field ratios and deviations from BCS predictions, extending understanding of superconductivity in these materials.

Findings

Reduced magnetic field ratio $h^*$ is universal and smaller than in conventional superconductors.

The temperature dependence of $H_{c2}$ deviates from BCS predictions even at large adiabaticity.

Results agree well with experimental data on TaP.

Abstract

Temperature dependence of the upper critical field $H_{c2}$ of the Dirac semi - metal (DSM) with phonon mediated pairing is considered within semi - classical approximation. The low temperature dependence deviates from conventional BCS superconductor with parabolic dispersion relation\cite{WHH} even for large adiabaticity parameter, $\gamma =\mu /\left( \hbar \Omega \right) $., where $\mu $ is the chemical potential and $\Omega $ - Debye frequency. In particular the "reduced field", ratio of zero temperature $% H_{c2}$ to derivative at critical temperature, $h^{\ast }=H_{c2}\left( 0\right) /\left( -T\frac{dH_{c2}}{dT}\right) |_{T_{c}}$, depends on $\gamma $ and can be extended beyond the adiabatic limit. The reduced magnetic field ratio is universal (independent of the chemical potential, interaction strength etc.) and smaller than the Werthamer ratio for clean superconductors: $h^{\ast }=0.55$ for DSM, $h^{\ast }\left( 0\right) =0.69$ for parabolic band. The results are in good agreement compared with recent experiments on $TaP$.