Theory of biexcitons and biexciton-exciton cascade in graphene quantum dots

Abstract

We present a microscopic theory of biexcitons in colloidal graphene quantum dots, and we discuss the possibility of a biexciton-exciton cascade generation. Assuming a ${p}_{z}$ orbital on each carbon atom, the single-particle properties are described in the tight-binding model. The screened direct, exchange, and scattering matrix elements of the Coulomb matrix are calculated using Slater ${p}_{z}$ orbitals. The many-body ground and excited states are constructed as a linear combination of a finite number of electron-hole pair excitations from the Hartree-Fock ground state by exact diagonalization techniques. The exciton and biexciton states are constructed exploiting the degeneracy of the valence- and conduction-band edges. The two degenerate exciton $(X)$ states and a corresponding biexciton $(XX)$ state are identified for generation of the $XX\text{\ensuremath{-}}X$ cascade in threefold-symmetric quantum dots. Finally, the Auger coupling of the $XX$ state with the excited $X$ states is predicted.