Role of confined phonons in thin film superconductivity

TL;DR

This paper investigates how confined phonons in thin film superconductors alter the electron pairing interactions, affecting the critical temperature and energy gaps, with a focus on the dependence on film thickness.

Contribution

It introduces a model accounting for quantized phonon spectra in thin films, revealing their impact on superconducting properties compared to bulk materials.

Findings

Confined phonons modify the electron-electron interaction in thin films.

Critical temperature $T_c$ depends on film thickness due to phonon confinement.

Superconducting energy gaps $ abla_n$ are affected by quantized phonon modes.

Abstract

We calculate the critical temperature $T_c$ and the superconducting energy gaps $\Delta_n$ of a thin film superconductor system, where $\Delta_n$ is the superconducting energy gap of the $n$-th subband. Since the quantization of both the electron energy and phonon spectrum arises due to dimensional confinement in one direction, the effective electron-electron interaction mediated by the quantized confined phonons is different from that mediated by the bulk phonon, leading to the modification of $T_c$ in the thin film system. We investigate the dependence of $T_c$ and $\Delta_n$ on the film thickness $d$ with this modified interaction.