Superconducting pairing symmetries of the Hubbard model on the honeycomb lattice with inhomogeneous hopping strength

Abstract

Using finite-temperature determinantal quantum Monte Carlo calculations, we find that the dominant pairing symmetries in the standard Hubbard model on the honeycomb lattice depend on the electron filling. When the electron density $\ensuremath{\rho}$ is larger than around 0.25, the dominant pairing symmetry is the $d+id$-wave; when the electron density is low enough ($\ensuremath{\rho}\ensuremath{\lesssim}0.25$), the dominant pairing symmetry is the $p+ip$ wave. For two electron densities $\ensuremath{\rho}=0.1$ and $\ensuremath{\rho}=0.4$, where the dominant pairing symmetries are $p+ip$ wave and $d+id$ wave separately, we study the effect of two types of hopping inhomogeneities (the plaquette and the quasi-$1\mathrm{D}$ hopping inhomogeneities) on the pairing symmetries. For $\ensuremath{\rho}=0.1$, the plaquette hopping inhomogeneity drives the dominant $p+ip$-wave pairing symmetry into the $d+id$-wave; while the quasi-$1\mathrm{D}$ hopping inhomogeneity almost does not affect the $p+ip$ wave, and arises the $f$ wave, causing the coexistence of $p+ip$-wave and $f$-wave pairing. For $\ensuremath{\rho}=0.4$, both the plaquette and the quasi-$1\mathrm{D}$ hopping inhomogeneities destroy the $d+id$-wave pairing symmetry, without causing other pairing symmetry. Our results suggest that the effect of hopping inhomogeneity on the pairing symmetries is robust and depends on the electron filling. This finding may be useful for the design of artificial graphene superconductors with different kinds of pairing, especially for the realization of the $d+id$-wave, $p+ip$-wave, or $f$-wave superconductors at low filling.