Edge effect and significant increase of the superconducting transition onset temperature of 2D superconductors in flat and curved geometries

TL;DR

This paper models how curvature in 2D superconductors can significantly enhance the transition temperature Tc, with spherical geometries showing the greatest increase due to phonon softening effects.

Contribution

It introduces a simple quantum mechanical model to demonstrate curvature-induced phonon softening and Tc enhancement in 2D superconducting geometries.

Findings

Curvature significantly increases Tc compared to flat geometries.

Hollow sphere exhibits the greatest Tc enhancement.

Edge effects cause broadening of Tc and influence phase fluctuations.

Abstract

In this paper, we present a simple method to model the curvature activated phonon softening in a 2D superconducting layer. The superconducting transition temperature Tc in the case of a 2D rectangular sheet, a hollow cylinder and a hollow sphere of one coherence length thickness is calculated by the quantum mechanical electron-phonon scattering matrix, and a series of collective lattice vibrations in the surface state. We will show that being extremely thin in a flat rectangular shape is not enough to significantly enhance the Tc through phonon softening. However, if a curvature is added, Tc can be strongly enhanced. The increase in Tc with respect to the bulk is greatest in a hollow sphere, intermediate in a hollow cylinder and weakest for the rectangular sheet, when systems of identical length scale are considered. In addition, we find that the edge effect of such a 2D sheet has a strong broadening effect on Tc in addition to the effect of order parameter phase fluctuations.