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We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the s-type Rydberg series of excitonic states follows a simple energy ladder: ǫn = −Ry * /(n + δ) 2 , n=1,2,. . . , in which Ry * is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is only accounted for by δ. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe2 ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schrödinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other, MoSe2, WS2, MoS2 MLs encapsulated in hBN, we estimate an apparent magnitude of δ for each of the studied structures. Intriguingly, δ is found to be close to zero for WSe2 as well as for MoS2 monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom.

We report on room-temperature Raman scattering measurements in few-layer crystals of exfoliated molybdenum ditelluride (MoTe2) performed with the use of 632.8 nm (1.96 eV) laser light excitation. In agreement with a recent study reported by G. Froehlicher et al 1 we observe a complex structure of the out-of-plane vibrational modes (A1g/A 1 ), which can be explained in terms of interlayer interactions between single atomic planes of MoTe2. In the case of low-energy shear and breathing modes of rigid interlayer vibrations, it is shown that their energy evolution with the number of layers can be well reproduced within a linear chain model with only the nearest neighbor interaction taken into account. Based on this model the corresponding in-plane and out-of-plane force constants are determined. We also show that the Raman scattering in MoTe2 measured using 514.5 nm (2.41 eV) laser light excitation results in much simpler spectra. We argue that the rich structure of the out-of-plane vibrational modes observed in Raman scattering spectra excited with the use of 632.8 nm laser light results from its resonance with the electronic transition at the M point of the MoTe2 first Brillouin zone.

Applications of two-dimensional (2D) perovskites have significantly outpaced the understanding of many fundamental aspects of their photophysics. The optical response of 2D lead halide perovskites is dominated by strongly bound excitonic states. However, a comprehensive experimental verification of the exciton fine structure splitting and associated transition symmetries remains elusive. Here we employ low temperature magneto-optical spectroscopy to reveal the exciton fine structure of (PEA) 2 PbI 4 (here PEA is phenylethylammonium) single crystals. We observe two orthogonally polarized bright in-plane free exciton (FX) states, both accompanied by a manifold of phonon-dressed states that preserve the polarization of the corresponding FX state. Introducing a magnetic field perpendicular to the 2D plane, we resolve the lowest energy dark exciton state, which although theoretically predicted, has systematically escaped experimental observation (in Faraday configuration) until now. These results corroborate standard multiband, effective-mass theories for the exciton fine structure in 2D perovskites and provide valuable quantification of the fine structure splitting in (PEA) 2 PbI 4 .