Orbital effect on the in-plane critical field in free-standing superconducting nanofilms

The superconductor to normal metal phase transition induced by the in-plane magnetic field is studied in free-standing Pb(111) nanofilms. In the considered structures, the energy quantization induced by the confinement leads to the thickness-dependent oscillations of the critical field (the so-called ''shape resonances''). In this paper, we examine the influence of the orbital effect on the in-plane critical magnetic field in nanofilms. We demonstrate that the orbital term suppresses the critical field and reduces the amplitude of the thickness-dependent critical field oscillations. Moreover, due to the orbital effect, the slope H_{c, parallel} - 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 analyzed. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)