Theoretical methods for excitonic physics in two-dimensional materials

TL;DR

This tutorial introduces various theoretical methods for calculating exciton properties in 2D materials, providing detailed guidance suitable for newcomers to perform research independently.

Contribution

It offers a comprehensive, detailed tutorial on analytical, semi-analytical, and numerical methods for exciton calculations in 2D materials, including explicit step-by-step procedures.

Findings

Application of methods to hBN and TMD monolayers

Solution of Bethe-Salpeter equation for biased bilayer graphene

Guidance enabling independent research in 2D excitonic physics

Abstract

In this tutorial we introduce the reader to several theoretical methods of determining the exciton wave functions and the corresponding eigenenergies. The methods covered are either analytical, semi-analytical, or numeric. We make explicit all the details associated with the different methods, thus allowing newcomers to do research on their own, without experiencing a steep learning curve. The tutorial starts with a variational method and ends with a simple semi-analytical approach to solve the Bethe-Salpeter equation in two-dimensional (2D) gapped materials. For the first methods addressed in this tutorial, we focus on a single layer of hexagonal Boron Nitride (hBN) and of transition metal dichalcogenide (TMD), as these are exemplary materials in the field of 2D excitons. For explaining the Bethe- Salpeter method we choose the biased bilayer graphene, which presents a tunnable band gap. The system has the right amount of complexity (without being excessive). This allows the presentation of the solution of the Bethe-Salpeter equation in a context that can be easily generalized to more complex systems or to apply it to simpler models.