Bending effects and optical properties of WSe2 nanoribbons of topological phase

A $\mathrm{W}{\mathrm{Se}}_{2}$ monolayer of $1{\mathrm{T}}^{\ensuremath{'}}$ phase is a large band-gap quantum spin Hall insulator, supporting dissipationless charge and spin transports through the topologically protected edge states. In this paper, we explore the nanoribbon forms of $1{\mathrm{T}}^{\ensuremath{'}}$-phase $\mathrm{W}{\mathrm{Se}}_{2}$ by first-principles density functional calculations and the many-body perturbation GW and Bethe-Salpeter equation method. We found that the $1{\mathrm{T}}^{\ensuremath{'}}$ $\mathrm{W}{\mathrm{Se}}_{2}$ nanoribbon can show topological edge states with a ribbon width of $\ensuremath{\sim}4\text{--}6\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$. Those edge bands show crossing through the Fermi level an odd number of times, with one kind of spin-polarization connecting the valence band and conduction band continua. The topological features of the edge bands hold even under small and medium bending in the nanoribbon, while large bending induces large band splitting, resulting in a topological switch-off in the edge bands. The semiconducting $1{\mathrm{T}}^{\ensuremath{'}}$ $\mathrm{W}{\mathrm{Se}}_{2}$ nanoribbon shows a large tunability with bending in optical absorption spectra and exciton states. The lowest-energy exciton is changed from optically dark in the flat nanoribbon to bright in the bent nanoribbons. These properties in the $1{\mathrm{T}}^{\ensuremath{'}}$ $\mathrm{W}{\mathrm{Se}}_{2}$ nanoribbons suggest potential applications in controllable quantum electronics and exciton-based quantum information processes.