Carrier Plasmon Induced Nonlinear Band Gap Renormalization in Two-Dimensional Semiconductors

Abstract

In reduced-dimensional semiconductors, doping-induced carrier plasmons can strongly couple with quasiparticle excitations, leading to a significant band gap renormalization. This effect has been long known and is essential for understanding transport and optical properties. However, the physical origin of this generic effect remains obscure. We develop a new plasmon-pole theory that efficiently and accurately capture this coupling. Using monolayer MoS 2 as a prototype two-dimensional (2D) semiconductor, we reveal a striking band gap renormalization around 400 meV and an unusual nonlinear evolution of its band gap with doping. This 2D prediction significantly differs from the linear behaviors that are common to one-dimensional structures. Our developed approach allows for a quantitative understanding of many-body interactions in general doped 2D semiconductors and paves the way for novel band gap engineering techniques.

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

“…Third, free carriers in low-dimensional systems form a low-energy acoustic plasmon which can dynamically couple with quasiparticles. These effects result in an enhanced many-body renormalization of quasiparticles energy, as shown from previous theoretical GW calculations in both semiconducting carbon nanotubes [21,22] and 2D transition metal dichalcogenides (TMDs) [23], and from experimental measurements [24][25][26][27]. More recently, beyond the nonlinear quasiparticle band gap renormalization of several hundred meV, the optical gap of monolayer TMDs was predicted to stay nearly constant due to a cancellation with the renormalization of exciton binding energy [28].…”

“…Although it has been shown that the true convergence of the band gap in MoS2 would require a much larger number of bands and dielectric cutoff [15], as far as our main concern of band gap renormalization goes, this set of parameters is enough. This is because the doping effect is mainly concentrated on small q and head (G=G'=0) part of the dielectric function ′ −1 ( , ) [23]. The dynamical part of the dielectric function is then constructed from the generalized plasmon-pole (GPP) model.…”

“…For a doped system, the change to the dielectric screening is concentrated on the head part of the dielectric function with small q and low frequency ω and requires a smaller number of bands to converge [23]. For this purpose, within the first-principles approach, the static dielectric function Following Ref.…”

“…For this purpose, within the first-principles approach, the static dielectric function Following Ref. [23], the GW self-energy of the doped system can be calculated according to Eq. (1) term by term.…”

“…In this work, we have developed an effective mass model and applied asymptotic analysis to resolve band gap renormalization, using the GW approximation and the framework of previous work [23]. The effective mass model supplements the ab initio calculation by bridging the gap around low doping density.…”