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 (∞ 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.