Electronic and vibrational properties of monolayer and bilayer TaSe$_2$*

Distinct from MoS$_2$, two-dimensional atomic crystal of tantalum diselenide (TaSe$_2$) is metallic and exhibits charge-density wave (CDW) transitions. Using density-functional theory, we present a first-principles study of the electronic and vibrational properties of monolayer and bilayer TaSe$_2$ without including the CDW-induced structural distortions. For monolayer 1T-TaSe$_2$, the frequencies of the Raman active modes are 159 cm$^{-1}$ ($E_g$) and 226 cm$^{-1}$ ($A_{1g}$), while the Raman-active modes for monolayer 2H-TaSe$_2$ are at 138 cm$^{-1}$ ($E''$), 214 cm$^{-1}$ ($E'$), and 241 cm$^{-1}$ ($A_1'$). For bilayer TaSe$_2$, different stackings of monolayer 2H-TaSe$_2$ and 1T-TaSe$_2$ phases have been calculated. Electronic band structures and vibrational properties of four energetically favorable configurations will be presented. Finally, the spin-orbit coupling on the structural and electronic properties will also be discussed.