Accurate and efficient description of interacting carriers in quantum nanostructures by selected configuration interaction and perturbation theory

Abstract

We present a method to calculate many-body states of interacting carriers in million atom quantum nanostructures based on atomistic tight-binding calculations and a combination of iterative selection of configurations and perturbation theory. This method enables investigations of large excitonic complexes and multi-electron systems with near full configuration interaction accuracy, even though only a small subspace of the full many-body Hilbert space is sampled, thus saving orders of magnitudes in computational resources. Important advantages of this method are that the convergence is controlled by a single parameter, the threshold, and that ground and excited states can be treated on an equal footing. We demonstrate the extreme efficiency of the method by numerical studies of complexes composed of up to 13 excitons, which requires filling of states up to the fourth electronic shell. We find that the method generally converges fast as a function of the threshold, profiting from a significant enhancement due to the perturbative corrections. The role of the choice of single-particle basis states is discussed. It is found that the algorithm converges faster in the Hartree-Fock basis only for highly charged systems, where Coulomb repulsion dominates. Finally, based on the observation that second order perturbative energy corrections only depend on off-diagonal elements of the many-body Hamiltonian, we present a way to accurately calculate many-body states that requires only a relatively small number of Coulomb matrix elements.