Renormalization of quasiparticle band gap in doped two-dimensional materials from many-body calculations

TL;DR

This paper introduces a first-principles effective-mass model within the GW approximation to accurately quantify doping-induced band gap renormalization in 2D materials, revealing the dominant many-electron interactions at different doping levels.

Contribution

It develops a computationally efficient model to predict band gap changes due to doping in 2D materials, clarifying the roles of Coulomb-hole and screened-exchange effects.

Findings

Band gap renormalization of a few hundred meV in 2D semiconductors.

Coulomb-hole dominates at low doping, screened-exchange at high doping.

Black phosphorus shows large renormalization due to its low density-of-states.

Abstract

Doped free carriers can substantially renormalize electronic self-energy and quasiparticle band gaps of two-dimensional (2D) materials. However, it is still challenging to quantitatively calculate this many-electron effect, particularly at the low doping density that is most relevant to realistic experiments and devices. Here we develop a first-principles-based effective-mass model within the GW approximation and show a dramatic band gap renormalization of a few hundred meV for typical 2D semiconductors. Moreover, we reveal the roles of different many-electron interactions: The Coulomb-hole contribution is dominant for low doping densities while the screened-exchange contribution is dominant for high doping densities. Three prototypical 2D materials are studied by this method, h-BN, MoS2, and black phosphorus, covering insulators to semiconductors. Especially, anisotropic black phosphorus exhibits a surprisingly large band gap renormalization because of its smaller density-of-state that enhances the screened-exchange interactions. Our work demonstrates an efficient way to accurately calculate band gap renormalization and provides quantitative understanding of doping-dependent many-electron physics of general 2D semiconductors.