Self-consistent tight-binding description of Dirac points moving and merging in two dimensional optical lattices

TL;DR

This paper develops an ab initio tight-binding model using Wannier functions to accurately describe the movement and merging of Dirac points in tunable honeycomb optical lattices, aligning well with experimental results.

Contribution

It introduces a first-principles tight-binding approach that precisely captures Dirac point dynamics in optical lattices, improving upon previous models.

Findings

Accurately reproduces Dirac point positions and merging behavior.

Calculates tunneling coefficients for various lattice configurations.

Provides high-precision spectrum predictions near Dirac points.

Abstract

We present an accurate ab initio tight-binding model, capable of describing the dynamics of Dirac points in tunable honeycomb optical lattices following a recent experimental realization [L. Tarruell et al., Nature 483, 302 (2012)]. Our scheme is based on first-principle maximally localized Wannier functions for composite bands. The tunneling coefficients are calculated for different lattice configurations, and the spectrum properties are well reproduced with high accuracy. In particular, we show which tight binding description is needed in order to accurately reproduce the position of Dirac points and the dispersion law close to their merging, for different laser intensities.