THE DIPOLAR FRENKEL EXCITONIC INSULATOR PHASE OF AN IMPURITY IN A LIQUID SOLVENT - THEORY

A theory of the dipolar Frenkel excitonic insulator (EI) phase develop ed in an earlier paper is extended to spatially disordered systems. Us ing the Hartree approximation studied previously, we derive, for a giv en atomic centre-of-mass configuration, a self-consistency equation fo r the atomic dipole moments, a non-zero solution to which indicates an EI phase. We obtain as a special case the microscopic Yvon-Kirkwood e quations of classical dielectric theory. For the experimentally releva nt case of an impurity at infinite dilution in a solvent or disordered matrix, we derive an explicit expression for the impurity dipole mome nt. To take into account the ensemble of atomic configurations a mean field approximation is developed, numerical results for which, within the class of linear approximations of classical liquid state theory, w ill be given in a subsequent paper. We also examine the dynamic respon se of the impurity system to an oscillating electric field. We locate the lowest excited state of the system in both the normal insulating a nd dipolar EI phases, and show that it is degenerate with the ground s tate at the EI transition, thus making contact with exciton theories o f the EI phase.