Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter

TL;DR

This paper proposes a novel Kekule-patterned superconducting phase on the honeycomb lattice of graphene, characterized by a spatially non-uniform, gapped, spin triplet state that breaks translational symmetry.

Contribution

It introduces the concept of Kekule order parameters as a new superconducting ground state on the honeycomb lattice, detailing phase transitions and topological excitations.

Findings

Transition from semimetal to p-Kekule superconductor with increasing attraction

Discontinuous transition from p-Kekule to s-Kekule superconductor

Discussion of topological excitations and competing states

Abstract

A spatially non-uniform superconducting phase is proposed as the electronic variational ground state for the attractive interactions between nearest neighbors on graphene's honeycomb lattice, close to and right at the filling one half. The state spontaneously breaks the translational invariance of the lattice into the Kekule pattern of bond order parameters, and it is gapped, spin triplet, and odd under the sublattice exchange. With the increase of attractive interactions we first find the transition from the semimetallic phase into the p-Kekule superconductor, defined as being odd under the exchange of Dirac points, with the additional discontinuous superconductor-superconductor transition into the even s-Kekule state, deep within the superconducting phase. Topological excitations of the Kekule superconductor and its competition with other superconducting states on the honeycomb lattice are discussed.