k-dependent SU(4) model of high-temperature superconductivity and its coherent-state solutions

We extend the SU(4) model [ Guidry et al. Phys. Rev. B 63 134516 (2001); Wu et al. Phys. Rev. B 67 014515 (2003); Guidry et al. Phys. Rev. B 70 184501 (2004); Sun et al. Phys. Rev. B 73 134519 (2006); Sun et al. Phys. Rev. B 75 134511 (2007)] for high-T_c superconductivity to an SU(4)_k model that permits explicit momentum (k) dependence in predicted observables. We derive and solve gap equations that depend on k, temperature, and doping from the SU(4)_k coherent states, and we show that the present SU(4)_k model reduces to the original SU(4) model for observables that do not depend explicitly on momentum. The results of the SU(4)_k model are relevant for experiments such as angle-resolved photoemission spectroscopy (ARPES) that detect explicitly k-dependent properties. The present SU(4)_k model describes quantitatively the pseudogap temperature scale and may explain why the ARPES-measured T^∗ along the antinodal direction is larger than the other measurements that do not resolve momentum. It also provides an immediate microscopic explanation for Fermi arcs observed in the pseudogap region. In addition, the model leads to a prediction that even in the underdoped regime, there exist doping-dependent windows around nodal points in the k space, where antiferromagnetism may be completely suppressed for all doping fractions, permitting pure superconducting states to exist.