Topological Properties of Bulk and Bilayer 2M WS$_2$: A First-Principles Study

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.