A phase formalism for excitonic transitions

V. A. Moskalenko

Vardan Apinyan, T. K. Kopeć

We study the excitonic phase transition in a system of the conduction band electrons and valence band holes described by the three-dimensional (3D) extended Falicov–Kimball (EFKM) model with the tunable Coulomb interaction $$U$$ between both species. By lowering the temperature, the electron–hole system may become unstable with respect to the formation of the excitons, i.e, electron–hole pairs at temperature $$T=T_{\Delta }$$ , exhibiting a gap $$\Delta $$ in the particle excitation spectrum. To this end we implement the functional integral formulation of the EFKM, where the Coulomb interaction term is expressed in terms of U(1) phase variables conjugate to the local particle number, providing a useful representation of strongly correlated system. The effective action formalism allows us to formulate a problem in the phase-only action in the form of the quantum rotor model and to obtain analytical formulas for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.

Walter Kohn

Mahito Mabuchi

Dynamical and statistical behaviors of Frenkel excitons in a matter system consisting of N two-level-atoms and interacting with an external field are studied with the molecular field and random phase approximations. Existence of a phase transition is suggested both in the exciton system and exciton-photon coupled system. This phase transition is the second order transition whose order parameter is the polarizability. A new type of condensation of the photon-exciton coupled wave, in which a macroscopic number of excitons and photons participate, has been found as a result of appreciable contribution of photons to the phase transition. When the incident light is coherent, the condition of phase transition is modified by photon induced exciton-exciton interaction. The energy dispersion of elementary excitations is derived.

Nguyễn Hồng Quang

The time evolution from coherent states to squeezed states of high density excitons is studied theoretically based on the boson formalism and within the Random Phase Approximation. Both the mutual interaction between excitons and the anharmonic exciton-photon interaction due to phase-space filling of excitons are included in consideration. It is shown that the exciton squeezing depends strongly on the exciton density in semiconductors and becomes smaller with increasing the latter.

Christo I. Ivanov, H. Barentzen, Marvin D. Girardeau