p-orbital density wave with d symmetry in high-Tc cuprate superconductors predicted by renormalization-group plus constrained RPA theory

The discovery of the charge-density-wave formation in the high-T-c cuprate superconductors has activated intensive theoretical studies for the pseudogap states. However, the microscopic origin of the charge-density-wave state has been unknown so far since the many-body effects beyond the mean-field-level approximations, called the vertex corrections, are essential. Toward solving this problem, we employ the recently developed functional renormalization group method, by which we can calculate the higher-order vertex corrections in a systematic and unbiased way with high numerical accuracy. We discover the critical development of the p-orbital-density-wave (p-ODW) instability in the strong-spin-fluctuation region. The obtained p-ODW state possesses the key characteristics of the charge-ordering pattern in Bi- and Y-based superconductors, such as the wave vector parallel to the nearest Cu-Cu direction, and the d-symmetry form factor with the antiphase correlation between p(x) and p(y) orbitals in the same unit cell. In addition, from the observation of the beautiful scaling relation between the spin susceptibility and the p-ODW susceptibility, we conclude that the main driving force of the density wave is the Aslamazov-Larkin vertex correction that becomes very singular near the magnetic quantum-critical point.