Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials

Abstract

We present a generalized hydrogen model for the binding energies ($E_B$) of excitons in two-dimensional (2D) materials that sheds light on the fundamental differences between excitons in two and three dimensions. In contrast to the well-known hydrogen model of three-dimensional (3D) excitons, the description of 2D excitons is complicated by the fact that the screening cannot be assumed to be local. We show that one can consistently define an effective 2D dielectric constant by averaging the screening over the extend of the exciton. For an ideal 2D semiconductor this leads to a simple expression for $E_B$ that only depends on the excitonic mass and the 2D polarizability $\alpha$. The model is shown to produce accurate results for 51 transition metal dichalcogenides. Remarkably, over a wide range of polarizabilities the expression becomes independent of the mass and we obtain $E_B^{2D}\approx 3/(4\pi \alpha )$, which explains the recently observed linear scaling of exciton binding energies with band gap. It is also shown that the model accurately reproduces the non-hydrogenic Rydberg series in WS${}_2$ and can account for screening from the environment.

5 pages

References in corpus (8)

• Quantum Spin Hall Effect and Topological Field Effect Transistor in Two-Dimensional Transition Metal Dichalcogenides
• Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
• Computational 2D Materials Database: Electronic Structure of Transition-Metal Dichalcogenides and Oxides
• Probing Excitonic Dark States in Single-layer Tungsten Disulfide
• Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2
• Measurement of high exciton binding energy in the monolayer transition-metal dichalcogenides WS2 and WSe2
• Excitons in van der Waals heterostructures: The important role of dielectric screening
• Linear density response function in the projector-augmented wave method: Applications to solids, surfaces, and interfaces

Cited by in corpus (67)

• The Computational 2D Materials Database: High-Throughput Modeling and Discovery of Atomically Thin Crystals
• Recent Progress of the Computational 2D Materials Database (C2DB)
• Layer-dependent properties of SnS2 and SnSe2 novel two-dimensional materials
• GPAW: An open Python package for electronic-structure calculations
• Interlayer excitons and Band Alignment in MoS${}_2$/hBN/WSe${}_2$ van der Waals Heterostructures
• Determination of layer-dependent exciton binding energies in few-layer black phosphorus
• The dielectric impact of layer distances on exciton and trion binding energies in van der Waals heterostructures
• 2D MoS2-Graphene-based multilayer van der Waals heterostructures: Enhanced charge transfer and optical absorption, and electric-field tunable Dirac point and band gap
• Electronic polarizability as the fundamental variable in the dielectric properties of two-dimensional materials
• Environmentally-Sensitive Theory of Electronic and Optical Transitions in Atomically-Thin Semiconductors
• Interlayer excitons in van der Waals heterostructures: Binding energy, Stark shift, and field-induced dissociation
• Magneto-optical response of chromium trihalide monolayers: chemical trends
• Polarons in two-dimensional atomic crystals
• Designing in-plane heterostructures of quantum spin hall insulators from first principles: 1T'-MoS2 with adsorbates
• The optical conductivity of few-layer black phosphorus by infrared spectroscopy
• Nonlinear optical selection rules of excitons in monolayer transition metal dichalcogenides
• Optical Absorption by Dirac Excitons in Single-Layer Transition-Metal Dichalcogenides
• Electron-phonon interaction and transport properties of metallic bulk and monolayer transition metal dichalcogenide TaS${}_2$
• Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides
• Gauge invariance of excitonic linear and nonlinear optical response
• Field-induced dissociation of two-dimensional excitons in transition-metal dichalcogenides
• Exciton formation assisted by longitudinal optical phonons in monolayer transition metal dichalcogenides
• Unified Treatment of Magnons and Excitons in Monolayer CrI${}_3$ from Many-Body Perturbation Theory
• Radiative lifetime of localized excitons in transition metal dichalcogenides
• Electrostatics of electron-hole interactions in van der Waals heterostructures
• Exciton in phosphorene: Strain, impurity, thickness and heterostructure
• Band nesting and exciton spectrum in monolayer MoS${}_2$
• Anisotropic Electron-Hole Excitation and Large Linear Dichroism in Two-Dimensional Ferromagnet CrSBr with In-Plane Magnetization
• Optical Properties of Anisotropic Excitons in Phosphorene
• Anomalous Non-Hydrogenic Exciton Series in 2D Materials on High-$\kappa$ Dielectric Substrates
• Cavity-induced exciton localisation and polariton blockade in two-dimensional semiconductors coupled to an electromagnetic resonator
• Quantum theory of two-dimensional materials coupled to electromagnetic resonators
• Substrate effects on the exciton fine structure of black phosphorus quantum dots
• Generalized scaling law for exciton binding energy in two-dimensional materials
• Exploration of the bright and dark exciton landscape and fine structure of MoS${}_2$ (using G${}_0$W${}_0$-BSE)
• Analytical description of the 1s exciton linewidth temperature-dependence in transition metal dichalcogenides
• Giant enhancement of exciton radiative lifetime by ferroelectric polarization: The case of monolayer TiOCl${}_2$
• Electronic Transport of Two-Dimensional Ultrawide Bandgap Material h-BeO
• Comment on "Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials"
• Combined tensor network/cluster expansion method using logic gates: Illustrated for (bi-)excitons by a single layer MoS${}_2$ model system
• Substrate Effect on Excitonic Shift and Radiative Lifetime of Two-Dimensional Materials
• Transition from band insulator to excitonic insulator via alloying Se into Monolayer TiS${}_3$: A Computational Study
• Two-dimensional excitons in monolayer transition metal dichalcogenides from simple models and variational calculations
• Photocatalytic Activity of Phosphorene Derivatives: Coverage, Electronic, Optical and Excitonic properties
• Substrate screening approach for quasiparticle energies of two-dimensional interfaces with lattice mismatch
• Isolating the Nonlinear Optical Response of a MoS${}_2$ Monolayer under Extreme Screening of a Metal Substrate
• Excitonic effects in time-dependent density functional theory from zeros of the density response
• Formation of dark excitons in monolayer transition metal dichalcogenides by a vortex beam: optical selection rules
• Anomalous energy shift of laterally confined two-dimensional excitons
• Dynamic polarizability of low-dimensional excitons
• Tunable effective masses of magneto-excitons in two-dimensional materials
• The effect of Non-centrosymmetricity on optical and electronic properties of cubic BaHfO${}_3$ perovskite structure
• 2-dimensional semiconductors pave the way towards dopant based quantum computing
• Conditions for the occurrence of Coulomb blockade in phosphorene quantum dots at room temperature
• Excitons in epitaxially grown WS2 on Graphene: a nanometer-resolved EELS and DFT study
• Efficient ionization of two dimensional excitons by intense single cycle terahertz pulses
• Analytical exciton energies in monolayer transition-metal dichalcogenides
• Finite-difference time-domain simulation of strong-field ionization: Perfectly matched layer approach
• Cosmic string influence on a 2D hydrogen atom and its relationship with the Rytova-Keldysh logarithmic approximation in semiconductors
• Exciton spectrum in two-dimensional transition metal dichalcogenides: The role of Diracness
• Strain-Enabled Giant Second-Order Susceptibility in Monolayer WSe${}_2$
• Retrieval of fundamental material parameters of monolayer transition metal dichalcogenides from experimental exciton energies: An analytical approach
• Canalized hyperbolic magnetoexciton polaritons enabled by the Shubnikov-de Haas effect in van der Waals semiconductors
• Layer-dependent Optical and Dielectric Properties of Large-size PdSe${}_2$ Films Grown by Chemical Vapor Deposition
• Strong 1D localization and highly anisotropic electron-hole masses in heavy-halogen functionalized graphenes
• Emergence of non-uniform strain induced exciton species in homo- and heterobilayer transition metal dichalcogenides
• Gauge-invariant optical selection rules for excitons