Electronic band gaps from Quantum Monte Carlo methods

TL;DR

This paper introduces a Quantum Monte Carlo method to accurately compute electronic band gaps in semiconductors and insulators, addressing finite size biases and validating results against experimental data.

Contribution

It presents a novel approach for calculating electronic gaps using grand canonical Quantum Monte Carlo with finite size corrections, improving accuracy over previous methods.

Findings

Finite size corrections significantly improve gap estimates.

Method successfully applied to solid molecular hydrogen.

Results agree well with experimental data for carbon and silicon.

Abstract

We develop a method for calculating the fundamental electronic gap of semiconductors and insulators using grand canonical Quantum Monte Carlo simulations. We discuss the origin of the bias introduced by supercell calculations of finite size and show how to correct the leading and subleading finite size errors either based on observables accessible in the finite-sized simulations or from DFT calculations. Our procedure is applied to solid molecular hydrogen and compared to experiment for carbon and silicon crystals.