Anomalous Non-Hydrogenic Exciton Series in 2D Materials on High-$\kappa$ Dielectric Substrates

TL;DR

This paper investigates how high-$7$ dielectric substrates alter exciton series in 2D materials, revealing a non-Hydrogenic behavior due to substrate-dominated screening effects, and provides an analytical model for exciton binding energies.

Contribution

It introduces a new understanding of exciton series behavior in 2D materials on high-$7$ dielectrics and derives an analytical expression for exciton binding energies.

Findings

Exciton Rydberg series becomes non-Hydrogenic on high-$7$ substrates.

Substrate screening causes higher excitonic states to be underbound.

Analytical formula for exciton binding energies in 2D materials is developed.

Abstract

Engineering of the dielectric environment represents a powerful strategy to control the electronic and optical properties of two-dimensional (2D) materials without compromising their structural integrity. Here we show that the recent development of high-$\kappa$ 2D materials present new opportunities for dielectric engineering. By solving a 2D Mott-Wannier exciton model for WSe$_2$ on different substrates using a screened electron-hole interaction obtained from first principles, we demonstrate that the exciton Rydberg series changes qualitatively when the dielectric screening within the 2D semiconductor becomes dominated by the substrate. In this regime, the distance dependence of the screening is reversed and the effective screening increases with exciton radius, which is opposite to the conventional 2D screening regime. Consequently, higher excitonic states become underbound rather than overbound as compared to the Hydrogenic Rydberg series. Finally, we derive a general analytical expression for the exciton binding energy of the entire 2D Rydberg series