Transport through a network of topological states in twisted bilayer graphene

Peter Rickhaus,¹ John Wallbank,² Sergey Slizovskiy,² Riccardo Pisoni,¹ Hiske Overweg,¹ Yongjin Lee,¹ Marius Eich,¹ Ming-Hao Liu,³ Vladimir Fal’ko,² Thomas Ihn,¹ and Klaus Ensslin¹

¹ Department of Physics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
²National Graphene Institute, University of Manchester, Manchester, M13 9PL,
³Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan

We show experimental transport data [1] on a particular interesting carbon system: Two minimally twisted layers of graphene [2,3].  Such a system exhibits a moiré superlattice with alternating AB and BA regions. For bernal-stacked bilayer graphene, first evidence of the Quantum valley hall effect along AB/BA stacking faults [4] has been reported recently. Similarly, a network of topological channels is predicted to occur in twisted bilayer graphene under a large interlayer bias [5]. We probe such a network with an electronic Fabry-Pérot interferometer [6,7]. The observed Fabry-Pérot and Aharanov-Bohm oscillations are robust in magnetic fields ranging from 0 to 8T, i.e. the trajectories in the bulk of the system cannot be bent by the Lorentz force. By extracting the enclosed length and area we find that the major contribution originates from trajectories encircling one row of AB/BA regions. The robustness in magnetic field and the linear spacing in density testifies to the fact that charge carriers flow in one-dimensional, topologically protected channels.