BCS-BEC crossover on the two-dimensional honeycomb lattice

TL;DR

This paper investigates the BCS-BEC crossover in the attractive Hubbard model on a honeycomb lattice, revealing how the crossover line passes through a quantum critical point and identifying collective modes relevant for experiments.

Contribution

It demonstrates the behavior of the BCS-BEC crossover near the quantum critical point on a honeycomb lattice and analyzes collective excitations like the Leggett mode.

Findings

Crossover line passes through the QCP at half-filling.

The Fermi surface area evolves nonmonotonically with interactions.

An undamped Leggett mode emerges deep in the superconducting phase.

Abstract

The attractive Hubbard model on the honeycomb lattice exhibits, at half-filling, a quantum critical point (QCP) between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half-filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the QCP at half-filling. For a range of densities around half-filling, the ``underlying Fermi surface'' of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which evolves nonmonotonically with interactions. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. We consider possible implications for experiments on ultracold atoms and high temperature SCs.