Two-Dimensional Valley Electrons and Excitons in Noncentrosymmetric 3R MoS${}_2$

Abstract

We find that the motion of the valley electrons -- electronic states close to the $\mathrm{K}$ and ${\mathrm{K}}^{\prime }$ points of the Brillouin zone -- is confined into two dimension when the layers of MoS${}_2$ follow the 3R stacking, while in the 2H polytype the bands have dispersion in all the three dimensions. According to our first-principles band structure calculations, the valley states have no interlayer hopping in 3R-MoS${}_2$, which is proved to be the consequence of the rotational symmetry of the Bloch functions. By measuring the reflectivity spectra and analyzing an anisotropic hydrogen atomic model, we confirm that the valley excitons in 3R-MoS${}_2$ have two-dimensional hydrogen-like spectral series, and the spreads of the wave function are smaller than the interlayer distance. In contrast, the valley excitons in 2H-MoS${}_2$ are well described by the three-dimensional model and thus not confined in a single layer. Our results indicate that the dimensionality of the valley degree of freedom can be controlled simply by the stacking geometry, which can be utilized in future valleytronics.

arXiv commentMain text: 5 pages, 4 figures, 3 tables. Supplemental Material: 2 pages, 1 figure. Submitted; Ver2: Discussion has been extended and Title has been changed upon publication

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• Tunable Berry curvature, valley and spin Hall effect in Bilayer MoS${}_2$
• Stacking-Dependent Interlayer Phonons in 3R and 2H MoS${}_2$
• Odd-parity superconductivity in bilayer transition metal dichalcogenides
• Unconventional superconducting gap structure protected by space group symmetry
• Control of interlayer delocalization in 2H transition metal dichalcogenides
• Interference of the Bloch phase in layered materials with stacking shifts
• Strong bilayer coupling induced by the symmetry breaking in the monoclinic phase of BiS${}_2$-based superconductors
• Multiple odd-parity superconducting phases in bilayer transition metal dichalcogenides
• Magneto-optical properties of bilayer transition metal dichalcogenides
• Second-harmonic imaging microscopy for time-resolved investigations of transition metal dichalcogenides