Superconductivity in lightly doped Hubbard model on honeycomb lattice

TL;DR

This study uses large-scale density-matrix renormalization group methods to investigate lightly doped Hubbard models on honeycomb lattices, revealing coexistence of superconducting and charge density wave orders with specific decay behaviors.

Contribution

It provides the first large-scale numerical evidence of superconductivity and charge density wave coexistence in the lightly doped honeycomb Hubbard model.

Findings

Superconducting and charge density wave correlations decay as power laws.

Spin-spin and single-particle correlations decay exponentially.

Coexistence of superconductivity and charge order observed.

Abstract

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.