Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials

Abstract

We present a generalized hydrogen model for the binding energies (EB) of excitons in twodimensional (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 EB that only depends on the excitonic mass and the 2D polarizability α. 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 2D B ≈ 3/(4πα), 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 WS2 and can account for screening from the environment.A striking property of two-dimensional semiconductors is the ability to form strongly bound excitons. This was initially predicted theoretically for hBN [1], graphane [2] and various transition metal dichalcogenides [3][4][5] and has subsequently been confirmed experimentally [6][7][8].The quantum confinement of excitons in 2D comprises a tempting and intuitively appealing explanation for the large binding energies in these materials [9]. However, it is now well understood that the confinement of the local electronic environment in 2D plays a crucial role in the formation of strongly bound excitons [3,10]. The 2D electronic system is rather poor at screening interactions and the effective Coulomb interaction between an electron and a hole is simply much stronger in 2D than in 3D.From a first principles point of view, the treatment of excitons requires advanced computational methodology such as the Bethe-Salpeter equation [11,12]. This approach has been applied to obtain absorption spectra for numerous insulators and usually yields very good agreement with experiments [13]. However, only systems of modest size can be treated this way and simplified models of excitons will be an inevitable ingredient in calculations of realistic systems. For example, if the effect of substrates or dielectric environment is to be included in the calculation of excitons in 2D systems [14], the computations become intractable with a standard BetheSalpeter approach. For three-dimensional materials the Mott-Wannier model comprises a strong conceptual and intuitive picture that provides a simple framework for calculating exciton binding energies [15]. In the center of mass frame, an excited electron-hole pair can be shown to satisfy a hydrogenic Schrödinger equation, where band structure effects are included through an excitonic effective mass µ and the dielectric screening from the environment is included through the static d...

Stark shift and electric-field-induced dissociation of excitons in monolayerMoS2andhBN/MoS2Haastrup1, Latini2, Bolotin3 et al. 2016Phys. Rev. BSelf Cite654491View full textAdd to dashboardCite

“…This is the so-called Mott-Wannier model which has been instrumental in the description of excitons in inorganic bulk semiconductors. A 2D version of the Mott-Wannier model has recently been shown to yield exciton binding energies in good agreement with BSE calculations and experiments for both freestanding [15,16,18,19,28] and supported [15,28,29] transition-metal dichalcogenide layers. The dissociation rate of the exciton is then obtained by complex scaling, which is a formally exact technique to compute resonance energies and lifetimes.…”

“…Recently, it has been shown that excitons in 2D materials can be described by a 2D hydrogen model with an effective dielectric constant [28], which for the linear screening described by Eq. (2) is given by eff = 1 2…”

Exciton formation assisted by longitudinal optical phonons in monolayer transition metal dichalcogenides

“…The bare Fröhlich interaction strengths obtained via ab initio techniques give 334 mev (MoS 2 ), 500 meV (MoSe 2 ), 140 mev (WS 2 ) and 276 meV (WSe 2 ) [70], hence the Molybdenum-based TMDCs possess higher exciton-phonon coupling strengths than the Tungsten-based TMDCs. A precise estimate of the exciton binding energy in the monolayer TMDCs is not available, however a range of binding energies (100 to 800 meV) have been reported for the monolayer systems [6,8,11,64,[64][65][66][78][79][80]. In order to compare the exciton formation rates between Molybdenum-based TMDCs and Tungsten-based TMDCs, we make use of the effective masses of electron and holes at the K energy valleys/peak position given in Ref.…”

Exciton Stark shift and electroabsorption in monolayer transition-metal dichalcogenides

“…These materials have intriguing electronic and optical properties and serve as versatile building blocks in van der Waals stacked devices [1][2]. The linear and nonlinear optical properties of semiconducting TMDs are dominated by excitons [1][2][3][4][5][6]. In monolayer structures with little substrate screening, the exciton binding energy is as large as 0.5 eV [3][4][5][6].…”