Pair density wave in the doped three-band Hubbard model on two-leg square cylinders

Abstract

A pair density wave (PDW) is a superconducting (SC) state with a spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been challenging. Here we report a density-matrix renormalization group study of a three-band Hubbard model (also known as the Emery model) for cuprates on long two-leg square cylinders. Upon light doping, we find that the ground state of the system is consistent with that of a PDW state with mutually commensurate and power-law SC, charge (CDW), and spin (SDW) density wave correlations. The SC correlations are dominant between neighboring Cu sites with $d$-wave pairing symmetry. Interestingly, we find that the near-neighbor interactions, especially the near-neighbor attractive ${V}_{pd}$ interaction between neighboring Cu and oxygen sites, can notably enhance the SC correlations while simultaneously suppressing the CDW correlations. For a modestly strong attractive ${V}_{pd}$, the SC correlations become quasi-long-ranged with a divergent PDW susceptibility.