Lattice distortions and stripes in the underdoped region of high-T_c cuprates

Superconducting and striped states under lattice distortions are investigated for high-T_c cuprates based on the quantum variational Monte Carlo method as the ground state of the two-dimensional (three-band) Hubbard model. We study the wavefunctions for the correlated condensed states: superconductivity, antiferromagnetism, inhomogeneity and their coexistent state with on-site Gutzwiller correlation. The model parameters are chosen for cuprate high-T_c superconductors such as La_1−xSr_xCuO₄ with x < 0.125. The ground state has vertical or horizontal hole-rich arrays coexisting with incommensurate magnetism and superconductivity (SC) in the low-temperature tetragonal (LTT) phase. We show that the total energy of the inhomogeneous d-wave SC state with vertical stripes having half-filled holes is lower than that of competing spin-density wave (SDW) states. The SC order parameter oscillates according to inhomogeneity in the antiferromagnetic background, and the SC condensation energy is reduced as the doping rate decreases in the underdoped region. The decreasing tendency of the SC condensation energy with decreasing doping is in accord with that of the specific heat data. In the low-temperature orthogonal (LTO) phase the diagonal stripes are stabilized in the lightly doped region for less than 5% doping. We also examine the stability of the mixed phase of LTT–HTT coexisting with stripes.