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

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 pz 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-X cascade in threefold-symmetric quantum dots. Finally, the Auger coupling of the XX state with the excited X states is predicted.