  Low-dimensional (LD) transition metal dichalcogenides (TMDs) in the form of
nanoflakes, which consist of one or several layers, are the subject of
intensive fundamental and applied research. Due to the size-induced transition
from a bulk to nanoscale, they can be both nonpolar, piezoelectric or even
ferroelectric. Also, in terms of electronic properties, they can be direct-band
semiconductors, semi-metals or even metals. The tuning of the electronic
properties in the LD-TMDs are commonly related with applied strains and strain
gradients, which can affect strongly their polar properties via the
piezoelectric and flexoelectric couplings. Using the density functional theory
(DFT) and phenomenological Landau approach, we studied the bended 2H-MoS$_2$
monolayer and analyzed its flexoelectric and piezoelectric properties. The
dependences of the dipole moment, strain and strain gradient on the coordinate
along the layer were calculated. From these dependences the components of the
flexoelectric and piezoelectric tensors have been determined and analyzed.
Obtained results are useful for applications of LD-TMDs in strain engineering
and flexible electronics.
