  We study dipole-mode and scissors-mode oscillations of a harmonically-trapped
dipolar supersolid, composed of dipolar droplets arranged on a one-dimensional
(1D) or a two-dimensional (2D) lattice, to establish the robustness of its
crystalline structure under translation and rotation, using a beyond-mean-field
model including a Lee-Huang-Yang interaction. The dipolar atoms are polarized
along the $z$ direction with the supersolid crystalline structure lying in the
$x$-$y$ plane. A stable dipole-mode oscillation was possible in case of both
quasi-1D and quasi-2D dipolar supersolids, whereas a sustained angular
scissors-mode oscillation was possible only in the case of a quasi-1D dipolar
supersolid between a maximum and a minimum of trap anisotropy in the $x$-$y$
plane. In both cases there was no visible deformation of the crystalline
structure of the dipolar supersolid during the oscillation. The theoretical
estimate of the scissors-mode-oscillation frequency was in good agreement with
the present results and the agreement improved with an increase of the number
of droplets in the supersolid and also with an increase in the confining trap
frequencies. The results of this study can be tested experimentally with
present knowhow.
