Density correlation function of a superlattice with wave function overlap

We have studied the electron density correlation function of a tunneling superlattice using a tight-binding envelope function and taking account of the nearest-neighbor overlap. A matrix density correlation function Π is introduced, which can be expressed explicitly in terms of a matrix density correlation bubble Π 0 and a matrix effective Coulomb potential V in RPA. The plasmon dispersion relation of a superlattice with electron wave function overlap, given by the equation det(1 − VΠ 0 )=0, is determined.