  Recently discovered 2M phase of bulk WS$_2$ was observed to exhibit
superconductivity with a critical temperature of 8.8 K, the highest reported
among superconducting transition metal dichalcogenides. Also predicted to
support protected surface states, it could be a potential topological
superconductor. In the present study, we perform a detailed first-principles
analysis of bulk and bilayer 2M WS$_2$. We report a comprehensive investigation
of the bulk phase, comparing structural and electronic properties obtained from
different exchange correlation functionals to the experimentally reported
values. By calculation of the $Z_2$ invariant and surface states, we give
support for its non-trivial band nature. Based on the insights gained from the
analysis of the bulk phase, we predict bilayer 2M WS$_2$ as a new
two-dimensional topological material. We demonstrate its dynamical stability
from first-principles phonon computations and present its electronic
properties, highlighting the band inversions between the W $d$ and S $p$
states. By means of $Z_2$ invariant computations and a calculation of the edge
states, we show that bilayer 2M WS$_2$ exhibits protected, robust edge states.
The broken inversion symmetry in this newly proposed bilayer also leads to the
presence of Berry curvature dipole and resulting non-linear responses. We
compute the Berry curvature distribution and the dipole as a function of Fermi
energy. We propose that BCD signals, which are absent in the centrosymmetric
bulk 2M WS$_2$, can be signatures of the bilayer. We hope our predictions lead
to the experimental realization of this as-yet-undiscovered two-dimensional
topological material.
