Magnetic-Field Oscillations of the Critical Temperature in Ultraclean, Two-Dimensional Type-I Superconductors

We investigate the influence of Landau Levels (LLs) and Zeeman energy, induced by an applied magnetic field B, on the critical temperature Tc for two-dimensional (2D) ultraclean superconductors using a fully quantum mechanical approach within the Bardeen–Cooper–Schrieffer (BCS) theory. In contrast to standard BCS theory, it allows for Cooper pair formation between electrons with opposite spins and momenta along the B direction, both on the same or on neighboring LLs. Our quantum mechanical treatment of LLs reveals that the critical temperature Tc for electrons paired on the same LL exhibits oscillations around the BCS critical temperature at low magnetic fields. The Zeeman energy leads to a decrease in Tc(B) with increasing B for electrons paired both on the same and on neighboring LLs. Notably, as the g-factor increases, Tc(B) decreases faster as the magnetic field increases for a larger g-factor than for a smaller one.