Magnetic properties of Type I and II Weyl Superconductors

TL;DR

This paper investigates the magnetic properties of Weyl superconductors of both type I and II, deriving a Ginzburg-Landau theory, analyzing vortex behavior, and comparing theoretical predictions with experimental data.

Contribution

It provides a microscopic phonon-mediated pairing model and a Ginzburg-Landau framework to understand the magnetic behavior of Weyl superconductors across topological transitions.

Findings

Superconductivity transitions from second to first kind near the topological transition at κ=1.

Critical fields Hc2 and Hc1 depend on the tilt parameter κ, matching experimental trends.

Thermal fluctuations can induce vortex lattice melting, with behavior differing between type I and II phases.

Abstract

Superconductivity was observed in certain range of pressure and chemical composition in Weyl semi-metals of both the type I and type II (when the Dirac cone tilt parameter $\kappa >1$). Magnetic properties of these superconductors are studied on the basis of microscopic phonon mediated pairing model. The Ginzburg - Landau effective theory for the order parameter is derived using Gorkov approach and used to determine anisotropic coherence length, the penetration depth determining the Abrikosov parameter for a layered material and applied to recent extensive experiments on $% MoTe_{2}$. It is found that superconductivity is of second kind near the topological transition at $\kappa =1$, but becomes first kind away from it. For the superconductors of the second kind the dependence of critical fields $H_{c2}$ and $H_{c1}$ on the tilt parameter $\kappa $ (governed by pressure) is compared with the experiments. Strength of thermal fluctuations is estimated and its is found that they are strong enough to cause Abrikosov vortex lattice melting near $H_{c2}$. The melting line is calculated and is consistent with experiments provided the fluctuations are three dimensional in the type I phase (large pressure) and two dimensional in the type II phase (small pressure).