Ballistic conductance in a topological 1$T'$-MoS$_2$ nanoribbon

A MoS$_2$ sheet in its 1$T'$ phase is a two-dimensional topological insulator. It possesses highly conductive edge states which due to topological protection, are insensitive to back scattering and are suitable for device channels. A transition between the topological and conventional insulator phases in a wide 1$T'$-MoS$_2$ sheet is controlled by an electric field orthogonal to the sheet. In order to enhance the current through the channel several narrow nanoribbons are stacked. We evaluate the subbands in a narrow nanoribbon of 1$T'$-MoS$_2$ by using an effective $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian. In contrast to a wide channel, a small gap in the spectrum of edge states in a nanoribbon increases with the electric field. It results in a rapid decrease in the nanoribbon conductance with the field, making it potentially suitable for switching.