Superconducting metallic nanofilms in the presence of in-plane magnetic field: orbital effect on the critical field and the multiband character of the Fulde-Ferrell-Larkin-Ovchinnikov state

P. Wójcik, M. Zegrodnik

Published 2014-12-14Version 1

The superconductor to normal metal phase transition induced by the in-plane magnetic field is studied in free-standing Pb(111) nanofilms. In such structures the energy quantization induced by the confinement leads to a multiband character of the system which results in the so-called shape resonances and the thickness-dependent oscillations of the critical field. First, we examine the influence of the orbital effect on the critical magnetic field and show that the orbital term suppresses the critical field (in comparison with the Pauli approximation) and reduces the amplitude of the thickness-dependent critical field oscillations. We demonstrate that due to the orbital effect, the slope $H_{c,||}-T_c$ at $T_c(0)$ becomes finite and decreases with increasing film thickness in agreement with recent experiments. The temperature $t^*$ at which the superconductor to normal metal phase transition becomes of the first order is also reduced by the orbital effect. Next, we focus on the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase and its interplay with the shape resonances as well as the influence of the multiband effects on its stability. We show that the range of the magnetic field for which the FFLO state is stable oscillates as a function of the film thickness with the phase shift equal to one half of the period corresponding to the critical magnetic field oscillations. Moreover, the multiband effects lead to a division of the FFLO phase stability region into subregions number of which depends on the number of bands participating in the paired state.