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

We study the properties of the upper critical field of superconductivity in nodal-line semimetals in a continuous model, which has a nodal-line on the $k_z=0$ plane. Using the semiclassical Green’s function method, we calculate the upper critical field for the two limiting cases: the dirty limit with many impurities and the clean limit with few impurities. The results show the large anisotropy of the magnitude of the upper critical field and the unusual temperature dependence. The obtained results are compared with recent experimental data of PbTaSe${}_2$.