Intersite Coulomb Interactions in Charge Ordered Systems

Using {\it ab initio} approaches for extended Hubbard interactions coupled to phonons, we reveal that the intersite Coulomb interaction plays important roles in determining various distinctive phases of the paradigmatic charge ordered materials of Ba$_{1-x}$K$_x A$O$_3$ ($A=$ Bi and Sb). We demonstrated that all their salient doping dependent experiment features such as breathing instabilities, anomalous phonon dispersions, and transition between charge-density wave and superconducting states can be accounted very well if self-consistently obtained nearest neighbor Hubbard interaction are included, thus establishing a minimal criterion for reliable descriptions of spontaneous charge orders in solids.