Band nesting and exciton spectrum in monolayer MoS2

Abstract

We discuss here the effect of band nesting and topology on the spectrum of excitons in a single layer of MoS2, a prototype transition metal dichalcogenide material. We solve for the single particle states using the ab initio based tight-binding model containing metal d and sulfur p orbitals. The metal orbitals contribution evolving from K to Γ points results in conduction-valence band nesting and a set of second minima at Q points in the conduction band. There are three Q minima for each K valley. We accurately solve the Bethe-Salpeter equation including both K and Q points and obtain ground and excited exciton states. We determine the effects of the electron-hole single particle energies including band nesting, direct and exchange screened Coulomb electron-hole interactions and resulting topological magnetic moments on the exciton spectrum. The ability to control different contributions combined with accurate calculations of the ground and excited exciton states allows for the determination of the importance of different contributions and a comparison with effective mass and k · p massive Dirac fermion models.

Trions in MoS$_2$ are quantum superpositions of intra- and intervalley spin states

“…However, unlike optically bright MoSe 2 , monolayer MoS 2 shows a large degree of valley polarization that is typically found in the optically dark materials, like WSe 2 and WS 2 . Importantly, recent experiments on magnetic brightening of dark excitons unequivocally showed an optically dark alignment with a splitting between 1s states of bright and dark excitons of ∆ db ∼ 14 meV [29], which is consistent with more recent theoretical work [33][34][35][36]. This value reflects both the SOC in the conduction band and the difference in the effective mass of the two subbands which leads to this inversion of ground state between single-particle and excitonic picture.…”

Rydberg series of dark excitons and the conduction band spin-orbit splitting in monolayer WSe2

“…Indeed, when assuming the theoretically calculated masses of a valence hole (0 C = 0.36) and electrons in two conduction subbands (0 D = 0.40 and 0 D = 0.29) 37 , we find > /> = 1.18, a value which is very close to the experimentally derived ratio / = 1.16. On the other hand, one may expect that the difference between and arises not only from the direct Coulomb term but also from the exchange term, as bright and dark excitons consist of parallel or antiparallel spin configurations, respectively [38][39][40] . Whereas we suggest here that the exchange term might be relatively small, this claim has be to taken with caution, since our estimations refer to theoretically calculated effective masses which perhaps are not sufficiently accurate (as inaccurate as the amplitude of the spin orbit splitting).…”

Fine structure of negatively charged and neutral excitons in monolayer MoS$_{2}$

“…It is worthwhile to mention that in this picture the energy of the spindown −K valley electron is above the spin-up empty electron state, thus, the order of the electron states is inverted and the lowest energy state is dark. We now explain [45] this bright-dark ground excitonic state inversion shown in figure 2(a). The first mechanism is related to different masses of spin-up and -down electrons in the conduction band.…”