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Synthesized micro- and nanotubes composed of transition metal dichalcogenides (TMDCs) such as MoS$_2$ are promising for many applications in nanophotonics, because they combine the abilities to emit strong exciton luminescence and to act as whispering gallery microcavities even at room temperature. In addition to tubes in the form of hollow cylinders, there is an insufficiently-studied class of twisted tubes, the flattened cross section of which rotates along the tube axis. As shown by theoretical analysis, in such nanotubes the interaction of electromagnetic waves excited at opposite sides of the cross section can cause splitting of the whispering gallery modes. By studying micro-photoluminescence spectra measured along individual MoS$_2$ tubes, it has been established that the splitting value, which controls the energies of the split modes, depends exponentially on the aspect ratio of the cross section, which varies in "breathing" tubes, while the relative intensity of the modes in a pair is determined by the angle of rotation of the cross section. These results open up the possibility of creating multifunctional tubular TMDC nanodevices that provide resonant amplification of self-emitting light at adjustable frequencies.

We show that the stacks of two-dimensional semiconductor crystals with the chiral packing exhibit optical activity and circular dichroism. We develop a microscopic theory of these phenomena in the spectral range of exciton transitions which takes into account the spin-dependent hopping of excitons between the layers in the stack and the interlayer coupling of excitons via electromagnetic field. For the stacks of realistic two-dimensional semiconductors such as transition metal dichalcogenides, we calculate the rotation and ellipticity angles of radiation transmitted through such structures. The angles are resonantly enhanced at the frequencies of both bright and dark exciton modes in the stack. We also study the photoluminescence of chiral stacks and show that it is circularly polarized., Comment: 10 pages, 6 figures