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

Journal Article · Fri Jun 04 00:00:00 EDT 2021 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.3.023173· OSTI ID:1786246

Kryjevski, Andrei ; Luu, Thomas ; Karasiev, Valentin

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. This is due to the oscillatory nature of the integrand exp(–S), where S is the imaginary-time action. This issue is a major obstacle to first-principles lattice quantum Monte Carlo studies of excited states of electrons in matter. However, in the Kohn-Sham orbital basis, which is the output of a density-functional theory simulation, the path integral for electrons in a semiconductor nanoparticle has only a mild fermion sign problem and is amenable to evaluation by standard stochastic methods. This is evidenced by our simulations of silicon hydrogen-passivated nanocrystals such as Si₃₅H₃₆,Si₈₇H₇₆,Si₁₄₇H₁₀₀, and Si₂₉₃H₁₇₂, which range in size 1.0–2.4 nm and contain 176 to 1344 valence electrons. We find that approximating the fermion action by its leading order polarization term results in a positive-definite integrand in the functional integral, and is a very good approximation of the full action. We compute imaginary-time electron propagators and extract the energies of low-lying electron and hole levels. Our quasiparticle gap predictions agree with the results of previous high-precision G₀W₀ calculations. This formalism allows calculations of more complex excited states such as excitons and trions.

• Research Organization: Univ. of Rochester, NY (United States). Lab. for Laser Energetics
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0003856
• OSTI ID: 1786246
• Alternate ID(s): OSTI ID: 1830715
• Journal Information: Physical Review Research, Journal Name: Physical Review Research Vol. 3 Journal Issue: 2; ISSN 2643-1564
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Electronic structure
First-principles calculations
Nanocrystals
Semiconductor compounds
Density functional calculations