Effects of dynamical dielectric screening on the excitonic spectrum of monolayer semiconductors

TL;DR

This paper introduces a numerical method to solve the dynamical Bethe-Salpeter Equation, revealing how dynamical dielectric screening affects exciton energies in monolayer semiconductors, including a counterintuitive blueshift phenomenon.

Contribution

The authors develop a new numerical approach to incorporate dynamical dielectric screening effects into excitonic spectral calculations in 2D materials.

Findings

Dynamical screening causes an exciton energy blueshift in supported monolayers.

Bandgap renormalization involves both low- and high-frequency dielectric constants.

The theory accurately predicts exciton energy shifts in various dielectric environments.

Abstract

We present a new method to solve the dynamical Bethe-Salpeter Equation numerically. The method allows one to investigate the effects of dynamical dielectric screening on the spectral position of excitons in transition-metal dichalcogenide monolayers. The dynamics accounts for the response of optical phonons in the materials below and on top the monolayer to the electric field lines between the electron and hole of the exciton. The inclusion of this effect unravels the origin of a counterintuitive energy blueshift of the exciton resonance, observed recently in monolayer semiconductors that are supported on ionic crystals with large dielectric constants. A surprising result is that while energy renormalization of a free electron in the conduction band or a free hole in the valence band is controlled by the low-frequency dielectric constant, the bandgap energy introduces a phase between the photoexcited electron and hole, rendering contributions from the high-frequency dielectric constant also important when evaluating self-energies of the exciton components. As a result, bandgap renormalization of the exciton is not the sum of independent contributions from energy shifts of the conduction and valence bands. The theory correctly predicts the energy shifts of exciton resonances in various dielectric environments that embed two-dimensional semiconductors.