Charge Density Waves on a Decorated Honeycomb Lattice

Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping t. The electron-electron interactions, if sufficiently large compared to this translationally invariant t, can give rise to ordered magnetic phases and Mott insulator transitions, especially at commensurate filling. The more complex situation of non-uniform t has been studied within a number of situations, perhaps most prominently in multi-band geometries where there is a natural distinction of hopping between orbitals of different degree of overlap. In this paper we explore related questions arising from the interplay of multiple kinetic energy scales and electron-phonon interactions. Specifically, we use Determinant Quantum Monte Carlo to solve the Holstein Hamiltonian on a `decorated honeycomb lattice', consisting of hexagons with internal hopping t coupled together by t'. This modulation of the hopping introduces a gap in the Dirac spectrum and affects the nature of the topological phases. We determine the range of t/t' values which support a charge density wave phase about the Dirac point of uniform hopping t=t' as well as the critical transition temperature T_c.