Merging and alignment of Dirac points in a shaken honeycomb optical lattice

TL;DR

This paper investigates how periodic shaking of a honeycomb optical lattice affects Dirac points, band structures, and phase transitions, using Floquet theory and considering interactions, with potential experimental observation via Raman spectroscopy.

Contribution

It introduces a comprehensive analysis of Dirac point merging, band structure modifications, and phase transitions in a shaken honeycomb optical lattice, including effects of next-nearest-neighbor hopping and interactions.

Findings

Dirac points can merge or align due to shaking-induced anisotropic hopping.

Next-nearest-neighbor hopping breaks particle-hole symmetry, leading to metallic phases.

Weak repulsive interactions influence density profiles and phase behavior.

Abstract

Inspired by the recent creation of the honeycomb optical lattice and the realization of the Mott insulating state in a square lattice by shaking, we study here the shaken honeycomb optical lattice. For a periodic shaking of the lattice, a Floquet theory may be applied to derive a time-independent Hamiltonian. In this effective description, the hopping parameters are renormalized by a Bessel function, which depends on the shaking direction, amplitude and frequency. Consequently, the hopping parameters can vanish and even change sign, in an anisotropic manner, thus yielding different band structures. Here, we study the merging and the alignment of Dirac points and dimensional crossovers from the two dimensional system to one dimensional chains and zero dimensional dimers. We also consider next-nearest-neighbor hopping, which breaks the particle-hole symmetry and leads to a metallic phase when it becomes dominant over the nearest-neighbor hopping. Furthermore, we include weak repulsive on-site interactions and find the density profiles for different values of the hopping parameters and interactions, both in a homogeneous system and in the presence of a trapping potential. Our results may be experimentally observed by using momentum-resolved Raman spectroscopy.