Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral
Abstract
In the Kohn-Sham orbital basis imaginary-time path integral for electrons in a semiconductor nanoparticle has a mild Fermion sign problem and is amenable to evaluation by the standard stochastic methods. This is evidenced by the simulations of silicon hydrogen-passivated nanocrystals, such as Si35H36,~Si87H76,~Si147H100 and Si293H172, which contain 176 to 1344 valence electrons and range in size 1.0 - 2.4~nm, utilizing the output of density functional theory simulations. We find that approximating Fermion action with just the leading order polarization term results in a positive-definite integrand in the functional integral, and that it is a good approximation of the full action. We compute imaginary-time electron propagators in these nanocrystals and extract the energies of low-lying electron and hole levels. Our quasiparticle gap predictions agree with the results of high-precision calculations using G0W0 technique. This formalism can be extended to calculations of more complex excited states, such as excitons and trions.