Momentum dependence of pseudo-gap and superconducting gap in variation theory

To consider the origin of a pseudo-gap and a superconducting gap found in the high-T-c cuprates, the momentum dependence of the singlet gap parameter and the superconductivity correlation function are evaluated in the t-J model by using an optimization variational Monte Carlo method. In the underdoped regime, the singlet gap is significantly modified from the simple d(x2-y2)-wave gap (proportional to cos k(x) - cos k(y)) by the contributions of long-range pairings. Its angular dependence along the Fermi surface is qualitatively consistent with those experimentally observed in both hole-and electron-doped cuprates. This singlet gap will correspond to the pseudo-gap and its doping dependence agrees with that of the pseudo-gap. On the other hand, the superconductivity correlation function is dominant in the nearest-neighbor pairing and its Fourier transform preserves the original simple d(x2-y2)-wave form. We argue that this superconductivity correlation function is closely related to the coherent superconductivity gap appearing below T-c in the 'Fermi arc' region. Its doping dependence is also consistent with the recent experimental observations.