Density Correlation Function in a Tunneling Superlattice with Electrons and Holes

We have studied the electron-electron, electron-hole and the hole-hole density correlation functions of the tunneling superlattice with electrons and holes by using the tight-binding envelope functions and taking account of the nearest-neighbor overlap. Based on a newly developed matrix separation technique, these density correlation functions can be explicitly expressed in terms of a matrix density correlation function which allows for a RPA calculation. An effective matrix screened carrier-carrier potential is introduced, which together with the matrix denmty correlation functions given in this paper provides a convenient way to study excitation, transport, and other propertics of a weak tunneling superlattice with both electrons and holes.