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We present an electrostatic theory of band gap renormalization in atomically-thin semiconductors that captures the strong sensitivity to the surrounding dielectric environment. In particular, our theory aims to correct known band gaps, such as that of the three-dimensional bulk crystal. Combining our quasiparticle band gaps with an effective mass theory of excitons yields environmentally-sensitive optical gaps as would be observed in absorption or photoluminescence. For an isolated monolayer of MoS 2 , the presented theory is in good agreement with ab initio results based on the GW approximation and the Bethe-Salpeter equation. We find that changes in the electronic band gap are almost exactly offset by changes in the exciton binding energy, such that the energy of the first optical transition is nearly independent of the electrostatic environment, rationalizing experimental observations.Introduction. Atomically-thin materials exhibit remarkable electronic properties due to their quasi-two-dimensional nature [1][2][3][4]. However, their size also makes them extremely sensitive to their local environment. A complete theoretical picture must simultaneously treat the two-dimensional nature of carriers and the dielectric character of the surroundings. This latter property is the primary distinction between atomically-thin materials (such as the transition metal dichalcogenides) and heterostructured semiconductor quantum wells (such as GaAs in AlGaAs).To date, many theoretical studies of atomically-thin materials have focused on the excitonic properties, including the large exciton binding energy [5][6][7], the unique excitonic Rydberg series [8,9], the nature of selection rules [10][11][12], and Berry phase modifications of the exciton spectrum [13,14]. Surprisingly, the quasiparticle band gap has received significantly less attention, especially from simplified microscopic theories, perhaps because it is challenging to measure experimentally. In fact, simple theories of the exciton binding energy are often times used in conjunction with the experimentally measured optical gap in order to estimate the quasiparticle band gap [8,15].The GW approximation represents the current method-ofchoice for the accurate calculation of band structures and band gaps [16,17]. However, the quasi-two-dimensional nature of the atomically-thin materials makes these calculations very challenging to converge [18][19][20]. In this work, we provide a simple electrostatic theory of band gap renormalization due to electrostatic proximity effects. Through combination with an effective mass theory of the exciton binding energy, we find that the optical gap -i.e. the sum of the band gap and the (negative) exciton binding energy -is extremely insensitive to the dielectric environment. To the best of our knowledge, this represents the first quasi-analytical demonstration of this remarkable effect.The band gap of nanoscale materials differs from that of the bulk parent material because of two separate effects: carrier confinement and dielectric con...

We present a many-body calculation of the band structure and optical spectrum of the layered hybrid organicinorganic halide perovskites in the Ruddlesden-Popper phase with the general formula A 2 A n−1 M n X 3n+1 , focusing specifically on the lead iodide family. We calculate the mean-field band structure with spin-orbit coupling, quasiparticle corrections within the GW approximation, and optical spectra using the Bethe-Salpeter equation. The model is parameterized by first-principles calculations and classical electrostatic screening, enabling an accurate but cost-effective study of large unit cells and corresponding thickness-dependent properties. A transition of the electronic and optical properties from quasi-two-dimensional behavior to three-dimensional behavior is shown for increasing n and the nonhydrogenic character of the excitonic Rydberg series is analyzed. The thickness-dependent 1s and 2s exciton energy levels are in good agreement with recently reported experiments and the 1s exciton binding energy is calculated to be 302 meV for n = 1, 97 meV for n = 5, and 37 meV for n = ∞ (bulk MAPbI 3 ).Hybrid organic-inorganic perovskites (HOIPs) are promising photovoltaic materials, most recently showing a high power conversion efficiency of over 24%. 1 A three dimensional bulk HOIP AMX 3 can be transformed into a layered HOIP in the Ruddlesden-Popper phase A 2 A n−1 M n X 3n+1 by substituting a small organic cation A + by a bulkier one A + .Common choices for the small organic cation are A + =CH 3 NH + 3 , NH + 4 ; for the bulkier cation are A + =C 4 H 9 NH + 3 , C 6 H 5 C 2 H 4 NH + 3 ; for the metal are M 2+ =Sn 2+ , Pb 2+ ; and for the halide are X − =Cl − , I − , Br − . A major drawback of the 3D HOIPs for photovoltaics is their relatively fast degradation when exposed to air, moisture, and light; in contrast, the layered HOIPs are more stable while maintaining high power conversion efficiencies under working conditions. 2,3 The optical properties of layered HOIPs can also be easily controlled by composition, 4 enhancing their flexibility for a variety of optoelectronic applications. Unlike the van der Waals materials -a prototypical family of layered materials including graphene, hexagonal boron nitride, and the transition-metal dichalcogenides -the layered HOIPs have sublayers that are covalently bonded. This distinct property makes the layered HOIPs an insightful mixeddimensional platform for investigating the transition of optoelectronic properties from two dimensional to three dimensional.The n-dependent properties of layered HOIPs have been experimentally investigated, especially during the last five years, 5-9 including mechanically exfoliated thin sheets of a layered HOIP. 10,11 Early theoretical investigations of the optical properties of layered HOIPs were performed using the effective mass approximation, giving good estimates for the exciton binding energy and a qualitative explanation of the essential physics. 5,12-14 For a quantitative analysis, ab initio approaches such as density functional...

We study the impact of organic surface ligands on the electronic structure and electronic band edge energies of quasi-two-dimensional (2D) colloidal cadmium selenide nanoplatelets (NPLs) using density functional theory. We show how control of the ligand and ligand–NPL interface dipoles results in large band edge energy shifts, over a range of 5 eV for common organic ligands with a minor effect on the NPL band gaps. Using a model self-energy to account for the dielectric contrast and an effective mass model of the excitons, we show that the band edge tunability of NPLs together with the strong dependence of the optical band gap on NPL thickness can lead to favorable photochemical and optoelectronic properties.

Silver phenylselenolate (AgSePh, also known as “mithrene”) and silver phenyltellurolate (AgTePh, also known as “tethrene”) are two-dimensional (2D) van der Waals semiconductors belonging to an emerging class of hybrid organic–inorganic materials called metal–organic chalcogenolates. Despite having the same crystal structure, AgSePh and AgTePh exhibit a strikingly different excitonic behavior. Whereas AgSePh exhibits narrow, fast luminescence with a minimal Stokes shift, AgTePh exhibits comparatively slow luminescence that is significantly broadened and red-shifted from its absorption minimum. Using time-resolved and temperature-dependent absorption and emission microspectroscopy, combined with subgap photoexcitation studies, we show that exciton dynamics in AgTePh films are dominated by an intrinsic self-trapping behavior, whereas dynamics in AgSePh films are dominated by the interaction of band-edge excitons with a finite number of extrinsic defect/trap states. Density functional theory calculations reveal that AgSePh has simple parabolic band edges with a direct gap at Γ, whereas AgTePh has a saddle point at Γ with a horizontal splitting along the Γ-N1 direction. The correlation between the unique band structure of AgTePh and exciton self-trapping behavior is unclear, prompting further exploration of excitonic phenomena in this emerging class of hybrid 2D semiconductors.