The dipolar Frenkel excitonic insulator phase of an impurity in a liquid solvent: theory

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Abstract
A theory of the dipolar Frenkel excitonic insulator (EI) phase developed in an earlier paper is extended to spatially disordered systems. Using the Hartree approximation studied previously, the authors derive, for a given atomic centre-of-mass configuration, a self-consistency equation for the atomic dipole moments, a non-zero solution to which indicates an EI phase. They obtain as a special case the microscopic Yvon-Kirkwood equations of classical dielectric theory. For the experimentally relevant case of an impurity at infinite dilution in a solvent or disordered matrix, they derive an explicit expression for the impurity dipole moment. 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, will be given in a subsequent paper. The authors also examine the dynamic response of the impurity system to an oscillating electric field. They locate the lowest excited state of the system in both the normal insulating and dipolar EI phases, and show that it is degenerate with the ground state at the EI transition, thus making contact with exciton theories of the EI phase.