Triangular lattice exciton model

TL;DR

This paper introduces a minimalistic triangular lattice model for semiconducting transition-metal dichalcogenides, capturing electron and exciton band structures with exchange interactions, bridging Wannier and Frenkel excitons.

Contribution

The model provides a simple yet effective way to derive exciton band structures, incorporating exchange interactions and environmental effects, aligning qualitatively with first-principles calculations.

Findings

Qualitative agreement with first-principles calculations.

Inadequacy of the 2D hydrogen model for lowest-energy excitons.

A-B exciton splitting depends on environment and spin-orbit coupling.

Abstract

We present a minimalistic equilateral triangular lattice model, from which we derive electron and exciton band structures for semiconducting transition-metal dichalcogenides. With explicit consideration of the exchange interaction, this model is appropriate across the spectrum from Wannier to Frenkel excitons. The single-particle contributions are obtained from a nearest-neighbor tight-binding model parameterized using the effective mass and spin-orbit coupling. The solutions to the characteristic equation, computed in direct space, are in qualitative agreement with first-principles calculations and highlight the inadequacy of the two-dimensional hydrogen model to describe the lowest-energy exciton bands. The model confirms the lack of subshell degeneracy and shows that the A-B exciton split depends on the electrostatic environment as well as the spin-orbit interaction.