Time-dependent density-matrix functional theory for biexcitonic phenomena

We formulate a time-dependent density-matrix functional theory (TDDMFT) approach for higher-order correlation effects like biexcitons in optical processes in solids based on a reduced two-particle density-matrix formalism within the normal orbital representation. A TDDMFT version of the Schrödinger equation for biexcitons in terms of one- and two-body reduced density matrices is derived, which leads to finite biexcitonic binding energies already with an adiabatic approximation. Biexcitonic binding energies for several bulk semiconductors are calculated using a contact biexciton model.

Figure 1

(Color online) Excitonic bound states in a two-level system with single-particle energies $E_1$ and $E_2$. $E_{\text{exc}}$ and $E_{\text{biexc}}$ are the binding energies of excitons and biexcitons, respectively. A biexcitonic state can be thought of as arising from a two-step process: First, two excitons are created, which then combine to form a biexciton whose energy is less than the energy of the two individual excitons.