Dirac Point Structure in a Bose-Einstein Condensate in a Honeycomb Optical Lattice

TL;DR

This paper investigates how interactions and lattice parameters affect Dirac points in a Bose-Einstein condensate within a honeycomb optical lattice, revealing interaction-insensitive Dirac points at zero momentum and topology changes at finite momentum.

Contribution

It demonstrates that Bose-Bose interactions modify Dirac cone velocities but do not alter Dirac point topology at zero momentum, while at finite momentum interactions can change Dirac point topology.

Findings

Dirac points appear at zero momentum for 0<β<2.

Interactions modify Dirac cone velocities but not topology at k=0.

Topology of Dirac points changes when condensate is at K point with weak interactions.

Abstract

We study the Bose-Einstein condensate in a honeycomb optical lattice within Bogoliubov theory and find that for a ${\bf k} = 0$ condensate, the Dirac points appear in the Bogoliubov excitation spectrum when $0 < \beta < 2$, which illustrates that the bose-bose interaction does not change the Dirac point structure but only give a modification of the velocity of the Dirac cone. When the bosons are driven to condense at ${\bf k} = {\bf K}$, however, we find that the topology of the Dirac points will be altered by arbitrary weak interaction. Furthermore, we find that the next-nearest-neighbor hopping in an isotropic and an anisotropic lattice has different effects to the dynamics of the condensate and it should be taken into account when the lattice is not sufficiently deep.