Model evidence of a superconducting state with a full energy gap in small cuprate islands

TL;DR

This paper explores the emergence of a fully gapped superconducting state in nanoscale cuprate islands, identifying surface-induced subdominant order parameters that depend on symmetry and align with experimental findings.

Contribution

It demonstrates how surface-induced $d_{x^2-y^2}+i s$ or $d_{x^2-y^2}+i d_{xy}$ order parameters can produce a global gap, explaining recent experimental observations in cuprate nanostructures.

Findings

Surface-induced $d_{x^2-y^2}+i s$ phase creates a spectroscopic gap.

Gap size increases with applied magnetic field.

The properties depend on the symmetry of the subdominant order parameter.

Abstract

We investigate subdominant order parameters stabilizing at low temperatures in nano-scale high-T$_c$ cuprate islands, motivated by the recent observation of a fully gapped state in nanosized YBa$_2$Cu$_3$O$_{7-\delta}$ [D. Gustafsson {\it et al}, Nature Nanotech. {\bf 8}, 25 (2013)]. Using complementary quasi-classical and tight-binding Bogoliubov-de Gennes methods, we show on distinctly different properties dependent on the symmetry being $d_{x^2-y^2}+i s$ or $d_{x^2-y^2}+i d_{xy}$. We find that a surface-induced $d_{x^2-y^2}+i s$ phase creates a global spectroscopic gap which increases with applied magnetic field, consistent with experimental observation.