Ab initio calculation of critical fields of superconductors

The upper critical field H_c2 is a key parameter for type-II superconductors, serving as a crucial indicator for technological applications. A reliable ab initio approach for predicting the critical field is highly desirable, as it could accelerate the design of functional superconductors. Here we present a simple and efficient density-functional-based method for calculating the enhancement of the Pauli-limiting field. There are two underlying assumptions—first, the material exhibits PT symmetry (P: parity; T: time reversal), ensuring that all electronic bands are Kramers degenerate; and secondly, the superconducting gap is spin-singlet and isotropic in momentum space. We then calculate how the degeneracy of each band is lifted in the presence of an external magnetic field, and average this effective g factor over the entire Fermi surface. The anisotropy of H_c2 is incorporated by considering the directionality of the magnetic field. We apply this method to cubic eta-carbide-type superconductors [1,2], including the recently discovered Ta₄Rh₂C [3].

[1] K. Ma et al., Chem. Mater. 33, 8722 (2021).

[2] H. Wu et al., Phys. Rev. B 111, 184506 (2025).

[3] K. Ma et al., Phys. Rev. Res. 7, 023147 (2025).