Superconductivity in the lightly doped Hubbard model on the cylindrical honeycomb lattice

We have performed large-scale density-matrix renormalization group studies of the lightly doped Hubbard model on the honeycomb lattice on long three- and four-leg cylinders. We find that the ground state of the system upon lightly doping is consistent with that of a superconducting state with coexisting quasi-long-range superconducting and charge density wave orders. Both the superconducting and charge density wave correlations decay as a power law at long distances with corresponding exponents ${K}_{sc}<2$ and ${K}_{c}<2$. On the contrary, the spin-spin and single-particle correlations decay exponentially, although with relatively long correlation lengths.