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

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As an extension of our previous work on the holon pairing instability in the t-J Hamiltonian [Phys. Rev. B 66, 054427 (2002)], we examine the orbital symmetries of holon pairing order parameters in high Tc 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 Tc. Finally we demonstrate that there exists no time-reversal symmetry breaking in association with the Cooper pair order parameter.