Chiral response in two-dimensional bilayers with time-reversal symmetry: A universal criterion

Chiral van der Waals bilayers with interlayer quantum coupling provide an exceptional platform for manipulating the intrinsic chirality within atomically thin films. In this paper, we delve into the intrinsic chirality of two-dimensional (2D) bilayers possessing time-reversal symmetry (TRS), based on the constitutive equations and circular dichroism (CD), using the methodologies pioneered in recent works by Stauber et al. [Phys. Rev. Lett. 120, 046801 (2018); Phys. Rev. B 98, 195414 (2018)]. We introduce chiral conductivity ${\ensuremath{\sigma}}_{\mathrm{chir}}$ and demonstrate that ${\ensuremath{\sigma}}_{\mathrm{chir}}\ensuremath{\ne}0$ leads to a nonzero CD, unveiling the distinctive chiral response inherent in a 2D bilayer. According to the criterion, to achieve a chiral response in 2D bilayers while preserving TRS, it is essential to eliminate both mirror and spatial inversion symmetries. Through the derivation of Poynting vectors, it becomes evident that ${\ensuremath{\sigma}}_{\mathrm{chir}}\ensuremath{\ne}0$ assumes a crucial role in realizing chiral plasmons within isotropy 2D bilayers characterized by TRS in the local response limit. We also simulate the chiral response of untwisted bilayer graphene under a bias voltage by means of numerical calculations.