Quantum size effects in thermodynamic superconducting properties of ultra thin films

TL;DR

This study uses multi-band BCS theory to analyze how ultra-thin film thickness influences superconducting properties, revealing oscillations in critical parameters and universal constants matching bulk values.

Contribution

It demonstrates the oscillatory behavior of thermodynamic properties with film thickness and confirms universal constants are unaffected by reduced dimensions.

Findings

Superconducting energy gap oscillates with film thickness.

Critical magnetic field and specific heat show oscillations as thickness varies.

Universal constants remain consistent with bulk superconductor values.

Abstract

By using multi-bands BCS theory, we have calculated the superconductivity energy gap and the critical temperature of a thin-film metallic superconductor. The thermodynamic superconducting characteristics such as critical magnetic field, specific heat, as well as the tunneling conductance are investigated for varying film thickness and temperature. We find the oscillation of thermodynamic superconducting properties with the film thickness, including the thermodynamic critical field $H_c$, the specific heat of normal, superconducting state, and position of the differential tunneling conductance peak. The two universal constants the nth sub-band energy gap $\Delta_n$ at temperature $T=0K$ over $k_BT_c$, and the specific heat jump at $T_c$ over normal state specific heat at $T_c$ are independent of the film thickness. Their values are the same as in the bulk superconductor.