Competing phases and suppression of superconductivity in hole-doped Hubbard model on honeycomb lattice

We investigate the hole-doped Hubbard model on a honeycomb lattice using a fermionic projected entangled pair states (fPEPS) method. Our study reveals the presence of quasi-long-range order of Cooper pairs, characterized by power-law decay of correlation functions with exponents K > 1. We further analyze the competing phases of superconductivity, specifically the antiferromagnetic (AFM) order and the charge density wave (CDW) order. Our results show that there are domain wall structures when the hole doping δ is small and the Coulomb parameter U is large. However, these structures disappear as we increase the hole doping δ or decrease U. Furthermore, for small hole doping, the system exhibits AFM order, which diminishes for δ > 0.05. Conversely, as the doping level increases, the CDW order gradually decreases. Notably, a considerable CDW order persists even at higher doping levels. These findings suggest a progressive suppression of the AFM order and a growing prominence of the CDW order with increasing δ.