Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral

Andrei Kryjevski; Thomas Luu; Valentin Karasiev

doi:10.1103/PhysRevResearch.3.023173

paper

Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral

arXiv:2003.01096 · doi:10.1103/PhysRevResearch.3.023173

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 $1.0 - 2.4 nm$ , 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 $G_{0} W_{0}$ technique. This formalism can be extended to calculations of more complex excited states, such as excitons and trions.

Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral

Abstract

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