Optoelectronics in two-dimensional materials

Abstract

Excitons, i.e. clusters of bound electrons and holes, and plasmons, collective oscillations of electronic density, play a fundamental role in light-matter interactions in semiconductor materials. We study excitonic complexes and plasmonic effects in two-dimensional van der Walls materials within many different contexts. We focus on materials that have recently attracted attention because of their interesting optoelectronic properties, such as graphene, few-layers black phosphorus, TMDCs, and their heterostructures. Initially, the role of dielectric screening of electron-hole interaction in van der Waals heterostructures is theoretically investigated. A comparison between models available in the literature for describing these interactions is made and the limitations of these approaches are discussed. A simple numerical solution of Poisson’s equation for a stack of dielectric slabs based on a transfer matrix method is developed, enabling the calculation of the electron-hole interaction potential at very low computational cost and with reasonable accuracy. Using different potential models, direct and indirect exciton binding energies in these systems are calculated within Wannier-Mott theory, and a comparison of theoretical results with recent experiments on excitons in two-dimensional materials is discussed. In parallel, the quantum electrostatic heterostructure (QEH) model enables an efficient computation of the wave vector and frequency-dependent dielectric function of layered van der Waals bonded heterostructures in terms of the dielectric functions of the individual layers, which are coupled classically via the electrostatic Coulomb interaction. Here we extend the QEH model by including (1) the contribution to the dielectric function from infrared active phonons of the 2D layers, (2) the possibility of including screening from homogeneous bulk substrates, and (3) the possibility to include intraband screening from free carriers in doped semiconducting layers. We demonstrate the potential of the QEH model by calculating the dispersion of electrostatically coupled phonons in multilayer stacks of hexagonal boron nitride (hBN), the strong hybridization of plasmons and optical phonons in graphene/hBN heterostructures including the surprisingly long ranged effect of a SiO$_2$ substrate, the effect of substrate screening on the exciton series of MoS$_2$, and the properties of hyperbolic plasmons in a doped phosphorene sheet. The new QEH code is distributed as a Python package with a simple command line interface and comprehensive library of dielectric building blocks are freely available providing an efficient open platform for modeling and design of vdW heterostructures. We employ the QEH method to explore the use of MoSSe Janus layers, which possess an intrinsic electric dipole caused by their out-of-plane structural asymmetry, to selectively dope graphene embedded inside a heterostructure without the need of external sources (such as electrostatic gates or chemical functionalization) in order to engineer graphene plasmons. We demonstrate that, through the control of the plasmon energy via the doping level and the hybridization of plasmons in different layers, we can reach graphene plasmon energies up to 0.5 eV or selectively quench certain (symmetric) modes by Landau damping. The possibility of using other Janus transition-metal dichalcogenides that could improve this effect is also investigated. Further work is then developed on the theoretical study of the effect of an external in-plane electric field on charged exciton states. These states are shown to be strongly bound so that electron hole dissociation is not observed up to high electric field intensities. Polarizabilities of excitons are obtained from the parabolicity of numerically calculated Stark shifts. For trions (charged excitons), however, a fourth order Stark shift is observed, which enables the experimental verification of hyperpolarizability in 2D materials, as observed in highly excited states of Rydberg series of atoms and ions. Moreover, such a high binding energy of charged excitons may allow for systems where trions are carried through the materials plane by an applied external field, which opens an avenue for possible novel optoelectronic device applications in the future.