Theory of Local Density of States of d-Wave Superconducting State Near the Surfaces of the t-J Model

TL;DR

This paper theoretically investigates how the local density of states near surfaces of d-wave superconductors varies with surface geometry, revealing zero-energy state formation, peak splitting, and spontaneous time-reversal symmetry breaking explained by a t-J model approach.

Contribution

It provides a microscopic understanding of surface states and symmetry breaking in high-Tc superconductors using a t-J model with Gutzwiller approximation.

Findings

Zero-energy states depend on surface geometry.

Large super-exchange interaction causes peak splitting.

Induced s-wave component explains symmetry breaking.

Abstract

Spatial dependencies of the pair potential and the local density of states near the surfaces of $d_{x^{2}-y^{2}}$-wave superconductors are studied theoretically. The calculation is based on the t-J model within a mean-field theory with Gutzwiller approximation. Various types of surface geometries are considered. Similar to our result in the extended Hubbard model, it is found that the formation of zero-energy states strongly depends on the surface geometry. In addition to this feature, the zero-energy states give peak splitting for the (110) surfaces when the super-exchange interaction $J$ is large. This is due to the induced s-wave component near the surface. The present result explains the microscopic origin of the spontaneous time- reversal symmetry breaking at the surfaces of high-$T_{c}$ superconductors.