  A WSe$_2$ monolayer shows many interesting properties due to its spin-orbit
coupling induced spin splitting in bands around the Fermi level and the
spin-valley configuration. The orientation of the spin polarization in the
relevant bands is crucial for the nature of exciton states and the optical
valley selectivity. In this work, we studied the WSe$_2$ nanoribbons under
different mechanical bending curvatures and electron/hole doping with density
functional theory and their optical absorption and excitonic states with
many-body perturbation GW and BSE (Bethe-Salpeter equation) methods. We found
that the WSe$_2$ nanoribbons can exhibit an enhanced SOC effect and a spatially
varying spin polarization in bands around the Fermi level under bending. The
spin-polarization can show an anisotropy (or asymmetry) in those nearly
degenerate bands, leading to a controllable magnetism via bending and
electron/hole doping to the nanoribbons, suggesting a potential application in
compact and controllable magnetic nanodevices and spintronics. The optical
absorption spectrum of the nanoribbon presents a large tunability with bending
within the near infrared region of about 0.4 to 1.5 eV, showing an enhanced
absorption at a large bending condition. The exciton states generally show
mixed or various spin configuration in the electron and hole pairs that are
controlled by bending, potentially useful for applications in spin-based
quantum information processes.
