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

TL;DR

This paper investigates how the orbital effect influences the in-plane critical magnetic field in free-standing superconducting nanofilms, revealing suppression of critical field oscillations and changes in phase transition behavior.

Contribution

It provides a detailed analysis of the orbital effect on critical fields and phase transition order in superconducting nanofilms, extending understanding of thickness-dependent phenomena.

Findings

Orbital effect suppresses critical field oscillations.

Finite slope of critical field-temperature near Tc due to orbital effect.

Transition to first-order phase transition at a specific temperature.

Abstract

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 $H_{c,||}-T_c$ 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.