A colloquium on the variational method applied to excitons in 2D materials
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THE EUROPEAN PHYSICAL JOURNAL B
Colloquium
A colloquium on the variational method applied to excitons in 2D materials Maurício F.C. Martins Quintela 1 and Nuno M.R. Peres 1,2,a 1 2
Centro de Física and Departamento de Física and QuantaLab, Universidade do Minho, 4710-057 Braga, Portugal International Iberian Nanotechnology Laboratory (INL), Av Mestre José Veiga, 4715-330 Braga, Portugal Received 18 September 2020 / Received in final form 2 November 2020 / Accepted 3 November 2020 Published online 2 December 2020 c EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature,
2020 Abstract. In this colloquium, we review the research on excitons in van der Waals heterostructures from the point of view of variational calculations. We first make a presentation of the current and past literature, followed by a discussion on the connections between experimental and theoretical results. In particular, we focus our review of the literature on the absorption spectrum and polarizability, as well as the Stark shift and the dissociation rate. Afterwards, we begin the discussion of the use of variational methods in the study of excitons. We initially model the electron–hole interaction as a soft-Coulomb potential, which can be used to describe interlayer excitons. Using an ansatz, based on the solution for the two-dimensional quantum harmonic oscillator, we study the Rytova–Keldysh potential, which is appropriate to describe intralayer excitons in two-dimensional (2D) materials. These variational energies are then recalculated with a different ansatz, based on the exact wavefunction of the 2D hydrogen atom, and the obtained energy curves are compared. Afterwards, we discuss the Wannier–Mott exciton model, reviewing it briefly before focusing on an application of this model to obtain both the exciton absorption spectrum and the binding energies for certain values of the physical parameters of the materials. Finally, we briefly discuss an approximation of the electron–hole interaction in interlayer excitons as an harmonic potential and the comparison of the obtained results with the existing values from both first-principles calculations and experimental measurements.
1 Introduction Alongside graphene, a wide range of bi-dimensional materials are currently studied and have a plethora of different physical properties and applications [1]. An important subclass of these materials is the family of transition-metal dichalcogenides with chemical formula MX2 , where M is a transition metal and X a chalcogen atom. These materials, specifically those with group-VI transition metals, are semiconductors which exhibit strong light-matter coupling, as well as having direct band gaps in the infrared and visible spectral regimes. Having been studied in their bulk form since the 1960’s [2,3], the advent of the study of two-dimensional (2D) layers with atomic scale thickness renewed the interest in these materials and their properties that make them good candidates for various applications in optics and
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