Honeycomb optical lattices with harmonic confinement

TL;DR

This paper investigates how Dirac points in a honeycomb optical lattice are affected by harmonic confinement, showing they persist locally and influence the spatial profile of a Fermi gas.

Contribution

It demonstrates that Dirac points survive under harmonic confinement and provides analytical and numerical methods to understand the density of states in such systems.

Findings

Dirac points persist locally in the trap

Density of states can be approximated by local density approximation

Distinct spatial profile of a noninteracting Fermi gas observed

Abstract

We consider the fate of the Dirac points in the spectrum of a honeycomb optical lattice in the presence of a harmonic confining potential. By numerically solving the tight binding model we calculate the density of states, and find that the energy dependence can be understood from analytical arguments. In addition, we show that the density of states of the harmonically trapped lattice system can be understood by application of a local density approximation based on the density of states of the homogeneous lattice. The Dirac points are found to survive locally in the trap as evidenced by the local density of states. They furthermore give rise to a distinct spatial profile of a noninteracting Fermi gas.