Twist, Slip, and Circular Dichroism in Van der Waals Bilayers

Stacking atomically thin 2D materials with a rotational misalignment between its layers produces a van der Waals bilayer in which all mirror symmetries can be broken. A fundamental experimental signature of a twisted multilayer is circular dichroism (CD): the conversion of a linearly polarized incident optical field to an elliptically polarized field in transmission. This work investigates the relation between CD, the twist angle and interlayer slip. In experiments where bilayers are formed by contacting one layer with another one has control of the relative rotation angle between the symmetry axes of each sheet, but not of lateral shifts between the layers. Accounting for the lateral shift the configuration space of the system introduces a phase degree of freedom which manifests in the CD and its frequency dependence. We demonstrate how the symmetry constraints in this expanded configuration space is manifest in CD in twisted bilayers as a function of rotation angle. We apply this approach to discuss twisted graphene bilayers and on bilayer transition metal dichalcogenides where the twist coherently couples the intralayer excitons of the two layers.