Time Reversal Symmetry Breaking States Near Grain Boundaries Between d-wave Superconductors

TL;DR

This paper investigates how grain boundaries between d-wave superconductors can induce broken time reversal symmetry, affecting the order parameter and density of states, even without complex order parameters.

Contribution

It demonstrates that time reversal symmetry can be broken near grain boundaries in d-wave superconductors without complex order parameters, under specific conditions.

Findings

Time reversal symmetry can be broken near grain boundaries.

Order parameter and density of states are affected by boundary conditions.

Broken symmetry occurs even with purely real d-wave order parameters.

Abstract

In this paper we study the order parameter and density of states near a grain boundary between two $d_{x^2-y^2}$ superconductors. We examine broken time reversal symmetry near the interface. In particular we show that, under suitable circumstances, time reversal symmetry must be broken even when the order parameter is purely $d_{x^2-y^2}$ everywhere in space.