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

Abstract

Dealing with both elemental and high- T c superconductors (SCs) - Sn, Nb and Pb belonging to the former category, and MgB 2 and different samples of YBCO to the latter - we show that the difference in the values of their critical magnetic field H c 1, c 2 and the penetration depth λ L (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 ( T c s). Based directly on the dynamics of pairing in a magnetic field and the corresponding number equation, our approach relates H c 1, c 2 of an SC with the following set of its properties: S 1 = { μ , T c , 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 H c 2 of an SC can be calculated via four different equations, each of which invokes two or more properties from its sample-specific set S 2 = { T c , gap , coherence length , λ L (0), jump in sp. ht. }, which is radically different from S 1 .