Reentrant high-magnetic field superconductivity in clean two-dimensional multiband metals near Lifshitz transition

We investigate the upper critical field in a clean two-dimensional multiple-band superconductor in the vicinity of the Lifshitz transition when one of the bands is very shallow. Due to small number of carriers in this band, the quasiclassical Werthamer-Helfand approximation[1] breaks down and Landau quantization has to be taken into account. Similar effects have been discussed before for single-band superconductors [2]. In multiple-band metal depletion of just one band may influence weakly the zero-field transition temperature but may strongly modify behavior in the magnetic field. We found that the transition temperature Tc2(H) has giant oscillations and is resonantly enhanced at the magnetic fields corresponding to full occupancy of the Landau levels in the shallow band. This enhancement is especially pronounced for the lowest Landau level. As a consequence, the reentrant superconducting regions in the temperature-field phase diagram emerge at low temperatures near the magnetic fields at which the chemical potential matches the Landau levels. These regions may be disconnected from the main low-field superconducting region. The specific behavior depends on the relative strength of the intraband and interband coupling constants. We also discuss the role of Zeeman spin splitting in the shallow band. The predicted behavior may realize in the gate-tuned FeSe monolayer.