Contribution to excitonic linewidth from free carrier–exciton scattering in layered materials: the example of hBN

Scattering of excitons by free carriers is a phenomenon, which is especially important when considering moderately to heavily doped semiconductors in low-temperature experiments, where the interaction of excitons with acoustic and optical phonons is reduced. In this paper, we consider the scattering of excitons by free carriers in monolayer hexagonal boron nitride encapsulated by a dielectric medium. We describe the excitonic states by variational wave functions, modeling the electrostatic interaction via the Rytova–Keldysh potential. Making the distinction between elastic and inelastic scattering, the relevance of each transition between excitonic states is also considered. Finally, we discuss the contribution of free carrier scattering to the excitonic linewidth, analyzing both its temperature and carrier density dependence.M.F.C.M.Q. acknowledges the International Nanotechnology Laboratory (INL) and the Portuguese Foundation for Science and Technology (FCT) for the Quantum Portugal Initiative (QPI) grant SFRH/BD/151114/2021. N.M.R.P. acknowledges support by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020, COMPETE 2020, PORTUGAL 2020, FEDER, and FCT through projects PTDC/FIS-MAC/2045/2021, EXPL/FIS-MAC/0953/ 2021, and from the European Commission through the project Graphene Driven Revolutions in ICT and Beyond (Ref. No. 881603, CORE 3)

A colloquium on the variational method applied to excitons in 2D materials

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.The authors thank Eduardo Castro and Joao Lopes dos Santos for comments on a preliminary version of this work, and Bruno Amorim for outlining the derivation in the Appendix A. N.M.R.P. acknowledges support from the European Commission through the project Graphene-Driven Revolutions in ICT and Beyond (Ref. No. 881603 - core 3), and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. In addition, funding from the projects POCI-01-0145-FEDER-028114, and POCI01-0145-FEDER-029265, and PTDC/NAN-OPT/29265/2017, and POCI-01-0145-FEDER-02888 is acknowledged