An Explanation of the Temperature-Dependent Upper Critical Field Data of H₃S on the Basis of the Thermodynamics of a Superconductor in a Magnetic Field

Excellent fits to a couple of the data-sets on the temperature (T)-dependent upper critical field (H_c2) of H₃S (critical temperature, T_c ≈ 200 K at pressure ≈ 150 GPa) reported by Mozaffari, et al. (2019) were obtained by Talantsev (2019) in an approach based on an ingenious mix of the Ginzberg-Landau (GL), the Werthamer, Helfand and Hohenberg (WHH), and the Gor’kov, etc., theories which have individually been employed for the same purpose for a long time. Up to the lowest temperature (T_L) in each of these data-sets, similarly accurate fits have also been obtained by Malik and Varma (2023) in a radically different approach based on the Bethe-Salpeter equation (BSE) supplemented by the Matsubara and the Landau quantization prescriptions. For T < T_L, however, while the (GL, WHH, etc.)-based approach leads to H_c2(0) ≈ 100 T, the BSE-based approach leads to about twice this value even at 1 K. In this paper, a fit to one of the said data-sets is obtained for the first time via a thermodynamic approach which, up to T_L, is as good as those obtained via the earlier approaches. While this is interesting per se, another significant result of this paper is that for T < T_L it corroborates the result of the BSE-based approach.