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

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.

Visualizing electrostatic gating effects in two-dimensional heterostructures

“…This behavior resembles the renormalization of the band gap due to freecarrier screening predicted in Ref. 35 .…”

“…In comparing features between photoemission, tunneling, optical and transport measurements, it is a challenge to account for differences in sample quality, dielectric environment, gate voltage and temperature [32][33][34][35][36] . An advantage of our technique is that these differences can be eliminated, since the same devices are also suitable for optical spectroscopy, and in principle for transport studies, which can be done under exactly the same conditions as the ARPES measurements.…”

Enhanced Electron-Phonon Interaction in Multivalley Materials

“…All these conclusions are fully consistent with what is known about monolayers of semiconducting TMDs. The energy difference ΔE ΓK reported in Table I from ARPES measurements is consistent with having only the K valley occupied upon accumulation of a density of holes reaching up to about 5 × 10 13 cm −2 [64,75,76]. Similarly, although no sufficiently systematic ARPES study of the conduction band of monolayer TMDs has been reported yet, analogous measurements on the doped surface of the bulk [77] (where doping should be limited to the first few layers) or monolayer [60] WSe 2 have shown that it is relatively easy to populate both the K and Q valleys in the conduction band (i.e., ΔE KQ in monolayer WSe 2 is significantly smaller than ΔE ΓK ; see Table I).…”

Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor

“…On the other hand, free carriers in both ReSe 2 and adjacent graphene can, in principle, contribute to the renormalization of E g and tunable E b in single-layer ReSe 2 . It has been predicted that E g of a free-standing 2D semiconductor can be substantially reduced because of the presence of free carriers ( 31 , 32 ). Further, the dominant contribution to the QP bandgap renormalization in these systems is predicted to arise from the Coulomb-hole self-energy and screened-exchange self-energy ( 31 ).…”

“…It has been predicted that E g of a free-standing 2D semiconductor can be substantially reduced because of the presence of free carriers ( 31 , 32 ). Further, the dominant contribution to the QP bandgap renormalization in these systems is predicted to arise from the Coulomb-hole self-energy and screened-exchange self-energy ( 31 ). However, a detailed analysis of the experimental data reveals that the renormalization of E g and tunable E b is not likely to arise from the presence of free carriers in ReSe 2 .…”