Absence of time-reversal symmetry breaking in association with the order parameter of Cooper pair in high $T_c$ superconductivity

TL;DR

This study investigates the orbital symmetries of holon pairing in high-temperature superconductors, revealing that the Cooper pair exhibits d-wave symmetry without breaking time-reversal symmetry.

Contribution

It extends previous work by analyzing the energy poles of the t-matrix to determine the orbital symmetries of holon pairing and their relation to the Cooper pair symmetry.

Findings

Both s- and d-wave symmetries occur at higher energy poles.

Only s-wave symmetry appears at the lowest energy pole.

No time-reversal symmetry breaking is associated with the Cooper pair.

Abstract

As an extension of our previous work on the holon pairing instability in the t-J Hamiltonian [Phys. Rev. B {\bf 66}, 054427 (2002)], we examine the orbital symmetries of holon pairing order parameters in high $T_c$ superconductivity by examining the energy poles of t-matrix. We find that both $s$- and d-wave symmetries in holon pair order parameter occur at low lying energy states corresponding to the higher energy poles of t-matrix while only the s-wave symmetry appears at the lowest energy pole and that this results in the d-wave symmetry in the Cooper pair order which is a composite of the holon pair of s-wave symmetry and the spinon pair of d-wave symmetry below $T_c$. Finally we demonstrate that there exists no time-reversal symmetry breaking in association with the Cooper pair order parameter.