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

TL;DR

This paper investigates the energy spectrum and bosonic excitations in a superfluid phase of two-dimensional graphene-type optical lattices, revealing how phase transition affects band structure and Dirac points.

Contribution

It provides a detailed analysis of the bosonic spectrum, including dispersion laws and spectral densities, using RPA and hard-core boson formalism, highlighting changes at the superfluid transition.

Findings

Number of subbands doubles in the superfluid phase

Dirac points survive only if subbands are energetically equivalent

Spectral densities are sensitive to temperature and chemical potential variations

Abstract

The energy spectrum of a system of Bose atoms in the superfluid phase in an optical lattice of the graphene type has been studied. The dispersion laws for the energy bands and the single particle spectral densities are calculated in the random phase approximation and in the framework of the hard-core boson formalism, and their changes at the transition from the normal phase to the superfluid one are described. As a result of this transformation, the number of subbands doubles. In the case of the subband energetic equivalence, the Dirac points in the spectrum survive, and their number becomes twice as much. When the subbands are energetically nonequivalent, the Dirac points are absent. The shape of spectral densities is shown to be sensitive to the changes in the temperature and the chemical potential position.