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

Andrei Kryjevski,Valentin Karasiev,Thomas Luu

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 $Si_{35}H_{36},~Si_{87}H_{76},~Si_{147}H_{100}$ and $Si_{293}H_{172},$ 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 $G_0W_0$ technique. This formalism can be extended to calculations of more complex excited states, such as excitons and trions.

Highlights

The fermion sign problem, when severe, prevents the computation of physical quantities of a system of interacting fermions via stochastic evaluation of its path integral
In recent years computational studies of atomistic models of these systems using ab initio electronic structure techniques have proven to be an attractive alternative to actual experiments as the ability to explore the vast set of possible configurations is inevitably limited
The most efficient comprehensive ab initio technique is based on many-body perturbation theory (MBPT), where density-functional theory (DFT) is augmented by the methods of perturbative many-body quantum mechanics

Summary

Introduction

The fermion sign problem, when severe, prevents the computation of physical quantities of a system of interacting fermions via stochastic evaluation of its path integral. Applications of semiconductor nanomaterials require quantitative understanding of their electronic structure including excited state properties. The resulting energies and wave functions are subsequently used in calculations of various excited-state properties (e.g., [16,17,18]).

Results

Conclusion