Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

Abstract

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS2, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron–electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe–Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

Spectroscopic Study of the Excitonic Structure in Monolayer MoS2 under Multivariate Physical and Chemical Stimuli

“…This result is confirmed by a recent theoretical work, where a tight‐binding approach was used to predict the ‐binding energy of monolayer on (0.226 eV) and monolayer encapsulated by hBN (0.178 eV). [ 60 ] We note that the resonances associated with the and states overlap energetically, which makes an experimental identification within PL spectra challenging.…”

Exciton spectrum in atomically thin monolayers: The role of hBN encapsulation

“…Consequently, the energy spectrum of the excitons in S-TMD MLs and hence their binding energy, defined as the energy difference between the electronic band gap and the ground 1s state, can be strongly modified by the used surrounding media of different dielectric responses. Whereas several scientific papers have focused on the effect of surrounding dielectrics on the excitonic ladder in MLs [20][21][22][23][24][25], there is a lack of analogous investigations of the thickness influence of the media enclosing S-TMD MLs. However, it is of utmost importance, as the highest quality MLs are obtained by their encapsulation in flakes of hexagonal BN (hBN), leading to a narrowing of excitonic resonances approaching the homogeneous linewidth limit [26][27][28].…”

Topologically Protected Photovoltaics in Bi Nanoribbons

“…The initial exciton | X ⟩ is taken as the bulk ground-state exciton false| X ⟩ Q = ∑ v , c , k A v c Q false( k false) c c k + Q † c v k | F S false⟩ which is a superposition of electron–hole pairs between any conduction ( c ) and valence ( v ) bands, excluding the edge bands . | FS ⟩ denotes the Fermi sea, and the coefficients A v c Q ( k ) which determine the exciton states are obtained by solving the Bethe–Salpeter equation. − Specifically, we assume that all orbitals are point-like, which greatly simplifies the calculation of the exciton spectrum. − Regarding screening, we use the Rytova–Keldysh potential. − The edge e–h pair is defined as false| s , s ′ , k ⟩ = c s k + Q † c s false′ k false| F S ⟩ where c s k + Q…”