A colloquium on the variational method applied to excitons in 2D materials
arXiv:2010.15749 · doi:10.1140/epjb/e2020-10490-9
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 \emph{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 \emph{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.
arXiv comment20 pages, 3 appendixes, 115 references, we welcome comments and suggestions for additional references
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Cited by in corpus (9)
- Theoretical methods for excitonic physics in two-dimensional materials
- Analytical description of the 1s exciton linewidth temperature-dependence in transition metal dichalcogenides
- Variationally optimized orbital approach to trions in two-dimensional materials
- Calculation of the nonlinear response functions of intra-exciton transitions in two-dimensional transition metal dichalcogenides
- Microscopic theory of the polarizability of transition metal dichalcogenides excitons: Application to WSe2
- Third-order polarizability of interlayer excitons in hetero-bilayers
- Sommerfeld enhancement factor in two-dimensional Dirac materials
- A perturbative approach to the polaron shift of excitons in transition metal dichalcogeniedes
- Tunable exciton polaritons in band-gap engineered hexagonal boron nitride