Theoretical analysis of anisotropic upper critical field in nodal-line semimetals

Nodal-line semimetals are semimetals in which a one-dimensional band intersection called a nodal-line exists due to a continuous series of band intersections. Some experiments have shown that the upper critical fields of superconductivities in nodal-line semimetals have unique behaviors. For example, PbTaSe₂ and SnTaS₂ are proposed to be nodal-line semimetals and show peculiar temperature dependence and anisotropy of the upper critical field.

In this study, we apply the quasiclassical Green's function method to an effective three-dimensional model of nodal-line superconductors. We performed the calculations under two different limits: the clean limit with few impurities and the dirty limit with many impurities. As a result, we found three features: (1) the anisotropy in the direction, (2) linear behavior at low temperatures, and (3) convex downward behavior near the critical temperature. These behaviors are different from those in ordinary s-wave superconductors but are consistent with the experiments of nodal-line superconductors. This suggests that the model used in this study is useful for analyzing the superconductivity in nodal-line semimetals.