Momentum dependence of pseudogap and superconducting gap in variation theory

To consider the origin of a pseudogap and a superconducting (SC) gap found in the high-T_c cuprates, we evaluated the momentum dependence of the singlet gap corresponding to the pseudogap and the SC gap in the t-J model, using an optimization variational Monte Carlo (VMC) method. In the underdoped regime, the singlet gap is significantly modified from the simple d_{x2 - y2}(d)-wave gap (∝ cos k_x - cos k_y) by the contribution of long-range pairings. Its angular dependence at the quasi Fermi surface is qualitatively consistent with those experimentally observed in both hole and electron-doped cuprates. On the other hand, a SC gap is almost unchanged, preserving the original simple d-wave form. Thus, it seems that the incoherent part of the singlet gap mainly influences the forms of observed gaps.