Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials

Choi, Jin Ho; Cui, Ping; Lan, Haiping; Zhang, Zhenyu

doi:10.1103/physrevlett.115.066403

Cited by 207 publications

(195 citation statements)

References 48 publications

Supporting

Mentioning

150

Contrasting

Order By: Relevance

“…4(a) we present the binding energy as a function of gap size for a wide range of two dimensional materials. In the absence of the anomalous exciton II, all binding energies fall close to a best fit line, a universal behaviour first noticed by Choi et al 27. In Fig.…”

Section: Resultssupporting

confidence: 83%

See 1 more Smart Citation

An anomalous interlayer exciton in MoS2

Azhikodan

Nautiyal

Shallcross

et al. 2016

Sci Rep

View full text Add to dashboard Cite

The few layer transition metal dichalcogenides are two dimensional materials that have an intrinsic gap of the order of ≈2 eV. The reduced screening in two dimensions implies a rich excitonic physics and, as a consequence, many potential applications in the field of opto-electronics. Here we report that a layer perpendicular electric field, by which the gap size in these materials can be efficiently controlled, generates an anomalous inter-layer exciton whose binding energy is independent of the gap size. We show this originates from the rich gap control and screening physics of TMDCs in a bilayer geometry: gating the bilayer acts on one hand to increase intra-layer screening by reducing the gap and, on the other hand, to decrease the inter-layer screening by field induced charge depletion. This constancy of binding energy is both a striking exception to the universal reduction in binding energy with gap size that all materials are believed to follow, as well as evidence of a degree of control over inter-layer excitons not found in their well studied intra-layer counterparts.

show abstract

Section: Resultssupporting

confidence: 83%

“…4(a) we include several additional materials to those considered in ref. 27 which both changes the slope of the universal line and worsens the fit, however to a good approximation the linear law still holds. What lies behind this universal relation discovered by Choi et al To answer this in panel (b) of Fig.…”

Section: Resultsmentioning

confidence: 98%

An anomalous interlayer exciton in MoS2

Azhikodan

Nautiyal

Shallcross

et al. 2016

Sci Rep

View full text Add to dashboard Cite

show abstract

“…[59][60][61] The parameters in this model, effective hole and electron mass along different crystallographic directions, and dielectric constant at zero frequency are calculated using HSE06 exchange-correlation functional. The obtained results for pristine SLP and BLP are in excellent agreement with previous GW-BSE results [49,50,62] and experimental measurement. [26] The calculated exciton binding E ex b is 0.76 eV, which confirm strongly bound exciton in SLP.…”

Section: Optical and Excitonic Propertiessupporting

confidence: 91%

Photocatalytic Activity of Phosphorene Derivatives: Coverage, Electronic, Optical and Excitonic properties

Arra¹,

Ramya²,

Babar³

et al. 2017

Preprint

View full text Add to dashboard Cite

In the context of two-dimensional metal-free photocatalyst, we investigate the electronic, optical and excitonic properties of phosphorene derivatives within first-principles approach. While two-dimensional phosphorene does not catalyze the complete water splitting reactions, O, S, and N coverages improve the situation drastically, and become susceptible to catalyze the complete reaction at certain coverages. We find that for all these dopants, 0.25 -0.5 ML coverages are thermodynamically more stable, and does not introduce midgap defect states and the composite systems remain semiconducting along with properly aligned valance and conduction bands. Further, within visible light excitation, the optical absorption remain very high 10 5 cm −1 in these composite systems, and the fundamental optical anisotropy of phosphorene remains intact. We also investigate the effect of layer thickness through bilayer phosphorene with oxygen coverages. Finally we investigate the excitonic properties in these composite materials that are conducive to both redox reactions.

show abstract

“…With the approximated expression (6), we obtain excellent agreement for binding energies up to ∼ 0.5 eV, whereas the binding energies are underestimated for strongly bound excitons. Recently, first principles calculations have indicated that exciton binding energies in different 2D materials scale linearly with the band gaps [19]. In the present model, this behavior comes out naturally since without local field effects, the in-plane components of the polarizability in the Random Phase Approximation are given by…”

mentioning

confidence: 76%

Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials

2016

View full text Add to dashboard Cite

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...

show abstract

Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials

Cited by 207 publications

References 48 publications

An anomalous interlayer exciton in MoS2

An anomalous interlayer exciton in MoS2

Photocatalytic Activity of Phosphorene Derivatives: Coverage, Electronic, Optical and Excitonic properties

Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials

Contact Info

Product

Resources

About