Flux Phase in Bilayer $t-J$ Model

TL;DR

This study investigates the flux phase in a bilayer $t-J$ model to understand time-reversal symmetry breaking near surfaces of high-$T_C$ cuprates, revealing conditions for spontaneous magnetic fields without local magnetization.

Contribution

It introduces the flux phase in a bilayer $t-J$ model as a possible explanation for surface time-reversal symmetry breaking in high-$T_C$ cuprates.

Findings

Flux phase can be stabilized near surfaces due to inhomogeneity.

Opposite signs of spontaneous magnetic fields in two layers can occur.

Surface states may violate ${ m T}$ symmetry without local magnetic fields.

Abstract

In order to study the time-reversal symmetry (${\cal T}$) breaking near a (110) surface of a high-$T_C$ cuprate YBCO, we consider the flux phase in a bilayer $t-J$ model. Although the stable solution in the bulk is the $d_{x^2-y-2}$-wave superconducting (SC) state, free energy of the flux phase is close to it, and thus the flux phase may occur when the SC order is disturbed by inhomogeneity, e.g., surface or impurity. It is found that, depending on the doping rate, the flux phase in which spontaneous magnetic fields in two layers have opposite signs may be stabilized. This may lead to a surface state with local ${\cal T}$ violation but without local magnetic field.