  Twisted bilayer structures have emerged as a fascinating arena in condensed
matter thanks to their highly tunable physics. The role of spin-orbit coupling
(SOC) in twisted bilayers has gained increasing attention due to its potential
for spintronics. Thus, it is appealing to propose new materials for
constructing twisted bilayers with substantial SOC. In this work, the
intriguing effects induced by twisting two layers of two-dimensional bismuthene
are unraveled from large-scale first-principles calculations. We show that
spin-orbit coupling significantly affects the electronic properties of twisted
bilayer bismuthene, even more than in its untwisted counterpart. We carefully
investigate how the interplay between the spin-orbit coupling and the twist
angle impacts the band structure and spin textures of twisted bilayer
bismuthene. We find that the twist angle can be deemed a control knob to switch
from a small-gap semiconductor to a metallic behavior. Most crucially, the
accurate analysis of the energy bands close to Fermi energy reveals a
twist-tunable splitting in the mexican-hat shape of the bands that can
otherwise be obtained only by applying enormous electric fields. Our
predictions provide insight into innovative bismuth-based technologies for
future spintronic devices.
