Investigation of the bosonic spectrum of two-dimensional optical graphene-type lattices. Normal phase

TL;DR

This study analyzes the bosonic band spectrum in two-dimensional honeycomb optical lattices, revealing how sublattice energies influence spectral gaps and Dirac points, with implications for understanding bosonic behaviors in graphene-like structures.

Contribution

It provides a detailed calculation of the bosonic spectrum and spectral densities in honeycomb optical lattices, highlighting the effects of on-site energy differences on spectral gaps and band structure.

Findings

Gapless spectrum with Dirac points at equivalent sites

On-site energy differences induce spectral gaps

Spectral density depends on chemical potential, gap, and temperature

Abstract

The band spectrum of bosonic atoms in two-dimensional honeycomb optical lattices with the graphene-type structure has been studied. The dispersion laws in the bands and the one-particle spectral densities are calculated for the normal phase in the random phase approximation. The temperature-dependent gapless spectrum with Dirac points located at the Brillouin zone boundary is obtained for the lattice with energetically equivalent sites, with the corresponding chemical potential lying outside the allowed energy band. Different on-site energies in the sublattices are shown to induce the appearance of a gap in the spectrum, so that the chemical potential can be located between the subbands, which gives rise to a substantial reconstruction of the band spectrum. The frequency dependences of the one-particle spectral density for both sublattices are determined as functions of the chemical potential level, the spectral gap magnitude, and the temperature.