  We study a periodic polaronic system, which exhibits a nanoscale superlattice
structure, as a model for hole-doped cuprates with checkerboard-like
heterogeneity, as has been observed recently by scanning tunneling microscopy
(STM). Within this model, the electronic and phononic excitations are
investigated by applying an unrestricted Hartree-Fock and a random phase
approximation (RPA) to a multiband Peierls-Hubbard Hamiltonian in two
dimensions.
