Electronic signatures of stacking domain boundaries in twisted bilayer graphene

Experiments on bilayer graphene (BLG) show the coexistence of regions of inequivalent stacking order (AB and BA) separated by domain boundaries, topological defects akin to solitons [1]. The Frenkel-Kontorova model predicts that in-plane atomic displacements result in stacking domain boundaries of few nanometers width. We show how a hexagonal network of stacking domain boundaries naturally arises in twisted BLG in the limit of small twist angle (below ca.~1$^{\circ}$). Equilibrium configurations of twisted BLG have been produced by means of classical force-field simulations. Atomic displacements diminish the area of AA stacking regions and extend the AB and BA stacking regions to triangular domains separated by boundaries of 7--8~nm width. Large-scale tight-binding simulations unveil the electronic properties of such twisted BLG models. A charge density depletion is the low-energy signature of stacking domain boundaries with electronic states mostly confined in AB and BA domains. Zero-energy states at the network nodes reach an asymptotic localization for vanishing twist angles. We propose STM experiments for confirming our predictions.\\[4pt] [1] L. Brown et al., Nano Lett. 12, 1609 (2012).\\[0pt] [2] J. S. Alden et al., PNAS 110, 11256(2013).\\[0pt] [3] J. Linang et al., Nano Lett. (2013).