Spectrum of exciton states in monolayer transition metal dichalcogenides: Angular momentum and Landau levels

Abstract

A four-band exciton Hamiltonian is constructed starting from the single-particle Dirac Hamiltonian for charge carriers in monolayer transition metal dichalcogenides (TMDs). The angular part of the exciton wave function can be separated from the radial part, in the case of zero center of mass momentum excitons, by exploiting the eigenstates of the total exciton angular momentum operator with which the Hamiltonian commutes. We explain why this approach fails for excitons with finite center of mass momentum or in the presence of a perpendicular magnetic field and present an approximation to resolve this issue. We calculate the (binding) energy and average interparticle distance of different excited exciton states in different TMDs and compare these with results available in the literature. Remarkably, we find that the intervalley exciton ground state in the ∓K valley has angular momentum j = ±1, which is due to the pseudospin of the separate particles. The exciton mass and the exciton Landau levels are calculated and we find that the degeneracy of exciton states with opposite relative angular momentum is altered by a magnetic field.

Theory of moiré localized excitons in transition metal dichalcogenide heterobilayers

“…46 and theoretically in Ref. 47. Moreover, the energy spacings between states 1s, 2s and 3s are a good match 48 to those reported in Ref.…”

Band nesting and exciton spectrum in monolayer MoS2

“…2p states in second excitonic shell 77 , also generated a lot of interest due to their novel topological properties [78][79][80] . The predicted splitting of the p-shell could be understood in terms of topological magnetic moments, consequence of Berry's geometric curvature, acting on finite angular momentum states as an effective magnetic field 81,82 . The same magnetic moments result in shift of the energy levels of s -series 83 , for which exciton's angular quantum number L is 0.…”

Foldy-Wouthuysen transformation for gapped Dirac fermions in two-dimensional semiconducting materials and valley excitons under external fields

“…A valley exciton is a Wannier-like exciton whose properties are decided by the additional valley degree of freedom and affected by the band-structure geometry [8][9][10][11][12][13]. Various physical phenomena related to valley excitons, such as Berry-curvature induced exciton energy-level splitting [14][15][16][17][18], valley-selected optical transition [9,10,19,20], exciton valley Hall effect [21,22], and exciton valley Zeeman effect [23][24][25][26][27] have been observed experimentally and discussed theoretically. While there are a lot of theoretical works using different methods to study different issues of valley excitons, the connection among different theories and interpretations is not manifest.…”

“…The Berry curvature effect on excitons in 2D materials has been studied theoretically [8, 14-17, 19, 20] and observed experimentally [18]. The Berrycurvature effect causes energy-level splitting [14][15][16][17][18] and anomalous selection rule [19,20] for valley excitons with nonzero angular momentum. It has been shown that the exciton Hamiltonian can be derived from a FW transformation of 2D gapped Dirac fermions [15,16].…”