Interplay of staggered flux phase andd-wave superconductivity

Abstract

We present a detailed study of the competition and interplay between the staggered flux phase ordering d-density wave (DDW) and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity within mean field theory. An analytic expression for the temperature dependence of the DDW order parameter is obtained. The strong competition between the two order parameters is demonstrated through their unusual temperature dependencies and its importance in calculating single-particle spectral function has been pointed out. In particular, it is shown that in a perfect square lattice with only nearest-neighbor hopping ${(t}_{1}),$ which preserves nesting of the Fermi surface, one of the order parameters is completely inhibited by the other (at a given concentration of hole). In this case the DDW state produces more of a ``real gap'' rather than a ``pseudogap'' in the quasiparticle energy. We demonstrate that a finite negative next-nearest-neighbor hopping ${(t}_{2})$ stabilizes the DDW state at underdoping, while very close to the half filling or well inside the underdoped regime, ${t}_{2}$ suppresses DDW order strongly and enhances superconductivity. The actual coexistence between the two orders is established only at finite ${t}_{2}.$ The superconducting ${T}_{c}$ is always found to be maximum at a doping concentration where the corresponding ${T}_{\mathrm{DDW}}$ goes to zero, the superconducting ${T}_{c}$ decreases on further increase of the doping concentration.