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 $S{i}_{35}{H}_{36},S{i}_{87}{H}_{76},S{i}_{147}{H}_{100}$ and $S{i}_{293}{H}_{172},$ which contain $176$ to $1344$ valence electrons and range in size $1.0-2.4nm$, 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 $G_0{W}_0$ technique. This formalism can be extended to calculations of more complex excited states, such as excitons and trions.