Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state

TL;DR

This paper investigates chiral d-wave superconductivity on the honeycomb lattice near the Mott state, demonstrating the stability of the d+id'-wave state across various interaction strengths and exploring the impossibility of mixed chirality states without symmetry breaking.

Contribution

It shows that the d+id'-wave superconducting state is favored on the honeycomb lattice near the Mott transition and rules out mixed chirality states in the t-J and Hubbard models without symmetry reduction.

Findings

d+id'-wave state is favored across a wide U range

Mixed chirality d-wave states are not possible without symmetry breaking

Extended unit cells do not stabilize zero chirality d-wave solutions

Abstract

We study superconductivity on the honeycomb lattice close to the Mott state at half-filling. Due to the sixfold lattice symmetry and disjoint Fermi surfaces at opposite momenta, we show that several different fully gapped superconducting states naturally exist on the honeycomb lattice, of which the chiral $d+id'$-wave state has previously been shown to appear when superconductivity appears close to the Mott state. Using renormalized mean-field theory to study the t-J model and quantum Monte Carlo calculations of the Hubbard-U model we show that the $d+id'$-wave state is the favored superconducting state for a wide range of on-site repulsion U, from the intermediate to the strong coupling regime. We also investigate the possibility of a mixed chirality d-wave state, where the overall chirality cancels. We find that a state with $d+id'$-wave symmetry in one valley but $d-id'$-wave symmetry in the other valley is not possible in the t-J model without reducing the translational symmetry, due to the zero-momentum and spin-singlet nature of the superconducting order parameter. Moreover, any extended unit cells result either in disjoint Dirac points, which cannot harbor this mixed chirality state, or the two valleys are degenerate at the zone center, where valley hybridization prevents different superconducting condensates. We also investigate extended unit cells where the overall chirality cancels in real space. For supercells containing up to eight sites, including the Kekul\'{e} distortion, we find no energetically favorable d-wave solution with an overall zero chirality within the restriction of the t-J model.