Coulomb effects in the absorbance spectra of two-dimensional Dirac materials

Abstract

A wide range of materials like graphene, topological insulators and transition metal dichalcogenides (TMDs) share an interesting property: the low energy excitations behave as Dirac particles. This emergent behavior of Dirac quasiparticles defines a large class of media that are usually called Dirac materials. The linear and nonlinear optical properties of Dirac materials with a gap are still largely unexplored, and in this Letter we build the foundations of a novel way to study the linear optical properties of these two-dimensional media. Our approach is based on a new Dirac-like formulation of the standard semiconductor Bloch equations used in semiconductor physics. We provide an explicit expression of the linear absorbance -- which we call the relativistic Elliott formula -- and use this to quantify the variation of the continuum absorbance spectrum with the strength of the Coulomb interaction (the Sommerfeld factor). Our calculations also show how the Coulomb enhancements scales with the bandgap and vanishes for zero bandgap, shedding new light on the behaviour of graphene for low light intensities. The results presented are in good quantitative agreement with published experimental results. Our new theory will allow researchers to explore the nonlinear interactions of intense, ultrashort pulses with TMDs, and the framework is flexible enough to be adapted to different experimental situations, such as cavities, multilayers, heterostructures and microresonators.

References in corpus (29)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Atomically thin MoS2: A new direct-gap semiconductor
• Universal Dynamic Conductivity and Quantized Visible Opacity of Suspended Graphene
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Two-Dimensional Material Nanophotonics
• Substrate-induced band gap opening in epitaxial graphene
• Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
• Optical Spectrum of MoS${}_2$: Many-body Effects and Diversity of Exciton States
• Measurement of the optical dielectric function of transition metal dichalcogenide monolayers: MoS2, MoSe2, WS2 and WSe2
• Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides
• Dirac materials
• Tight-binding model and direct-gap/indirect-gap transition in single-layer and multi-layer MoS${}_2$
• Carrier Multiplication in Graphene
• Elastic scattering theory and transport in graphene
• Analytical approach to excitonic properties of MoS2
• Theory of second harmonic generation in few-layered MoS2
• Why does graphene behave as a weakly interacting system?
• Influence of the effective layer thickness on the groundstate and excitonic properties of transition-metal dichalcogenide systems
• Excitonic effects in the optical properties of 2D materials: An equation of motion approach
• Excitonic structure of the optical conductivity in MoS${}_2$ monolayers
• Optical Absorption by Dirac Excitons in Single-Layer Transition-Metal Dichalcogenides
• Model Prediction of Self-Rotating Excitons in Two-Dimensional Transition-Metal Dichalcogenides
• Measurement of the surface susceptibility and the surface conductivity of atomically thin $\mathrm{Mo}{\mathrm{S}}_2$ by spectroscopic ellipsometry
• Measure of Diracness in two-dimensional semiconductors
• Excitonic Collapse in Semiconducting Transition Metal Dichalcogenides
• Optically bright $p$-excitons indicating strong Coulomb coupling in transition-metal dichalcogenides
• THz driven quantum wells: Coulomb interactions and Stark shifts in the ultrastrong coupling regime
• The Nonlinear Optical Effects of Opening a Gap in Graphene

Cited by in corpus (5)

• Exciton oscillator strength in two-dimensional Dirac materials
• Optotwistronic of bilayer graphene
• Effect of intravalley and intervalley electron-hole exchange on the nonlinear optical response of monolayer MoSe${}_2$
• Sommerfeld enhancement factor in two-dimensional Dirac materials
• Long-lived Nonlinear Oscillatory States in Interacting Relativistic Bose-Einstein Condensates