  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.
