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arXiv · 2202.12010

Theoretical methods for excitonic physics in two-dimensional materials

M. F. C. Martins Quintela·J. C. G. Henriques·N. M. R. Peres
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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.

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M. F. C. Martins Quintela, J. C. G. Henriques, N. M. R. Peres. 2022-02-24. Theoretical methods for excitonic physics in two-dimensional materials. https://doi.org/10.1002/pssb.202200097

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