On the Role of Chemical Potential in Determining the Temperature Dependent Critical Magnetic Field and the Penetration Depth of Superconductors

Dealing with both elemental and high-Tc superconductors (SCs) - Sn, Nb and Pb belonging to the former category, and MgB2 and different samples of YBCO to the latter - we show that the difference in the values of their critical magnetic field Hc1,c2 and the penetration depth λL(0) is, remarkably, attributable predominantly to the difference in the values of a single parameter, viz., the chemical potential (μ) close to their critical temperatures (Tcs). Based directly on the dynamics of pairing in a magnetic field and the corresponding number equation, our approach relates Hc1,c2 of an SC with the following set of its properties: S1 = {μ, Tc, Debye temperature, effective mass of the electron, magnetic interaction parameter, Landau index}. Hence, it provides an alternative to the approach followed by Talantsev [Mod. Phys. Lett. B 33, 1950195 (2019)] who has shown by ingeniously combining the results of various well-established theories that Hc2 of an SC can be calculated via four different equations, each of which invokes two or more properties from its sample-specific set S2 = {Tc, gap, coherence length, λL(0), jump in sp. ht.}, which is radically different from S1.

A Dynamical Approach to the Explanation of the Upper Critical Field Data of Compressed H3S

Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (Hc2(T)) data of H3S reported by Mozaffari et al. [Nature Communications 10, 2522 (2019)] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S1 = {Tc, gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of Hc2(T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μ- and m*-dependent equation for Hc2(T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model. For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of Hc2(0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S2 = {μ, m*, interaction parameter λm, Landau index NL}, which is altogether different from S1.