Cooperative orbital moments and edge magnetoresistance in monolayer WTe${}_2$

We argue that edge electrons in monolayer WTe${}_2$ can possess a “cooperative” orbital moment (COM) that critically impacts its edge magnetoresistance behavior. Arising from the cooperative action of both Rashba and Ising spin orbit coupling, COM quickly achieves large magnitudes (of order few Bohr magnetons) even for relatively small spin-orbit coupling strengths. As we explain, such large COM magnitudes arise from an unconventional cooperative spin canting of edge spins when Rashba and Ising spin orbit coupling act together. Strikingly, COM can compete with spin moments to produce an unusual anisotropic edge magnetoresistance oriented at an oblique angle. In particular, this competition produces a direction along which $\mathbf{B}$ is ineffective at gapping out the edge spectrum leaving it nearly gapless. As a result, large contrasts in gap sizes manifest as $\mathbf{B}$ is rotated granting giant anisotropic magnetoresistance of 0.1-10 million % at 10 T and low temperature.