Chirality in twisted bilayer graphene

We derive a simple formula for the real-space chirality of twisted bilayer graphene and observe a sign-change due to an emergent C₆-symmetry. Surprisingly, this change occurs at roughly the same twist angle for Fermi energies up to E_F~75meV, see Figure 1. Our observation thus offers a new definition of the magic angle based on a macroscopic observable which is accessible in typical transport experiments [1]. We further predict an unprecedented large local chirality for the plasmonic near-field when sufficiently screened. Twisted bilayer graphene or other twisted two-dimensional heterostructure might thus provide a novel platform to catalyze the reaction of new chiral molecules while conserving time-reversal symmetry [2].
[1] T. Stauber, J. González, and G. Gómez-Santos, Phys. Rev. B 102, 081404(R) (2020)
[2] T. Stauber, T. Low, and G. Gómez-Santos, arXiv:2009.00478