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We investigate transport in the network of valley Hall states that emerges in minimally twisted bilayer graphene under interlayer bias. To this aim, we construct a scattering theory that captures the network physics. In the absence of forward scattering, symmetries constrain the network model to a single parameter that interpolates between one-dimensional chiral zigzag modes and pseudo-Landau levels. Moreover, we show how the coupling of zigzag modes affects magnetotransport. In particular, we find that scattering between parallel zigzag channels gives rise to Aharonov-Bohm oscillations that are robust against temperature, while coupling between zigzag modes propagating in different directions leads to Shubnikov-de Haas oscillations that are smeared out at finite temperature.
We study the electronic transport properties at the intersection of three topological zero-lines as the elementary current partition node that arises in minimally twisted bilayer graphene. Unlike the partition laws of two intersecting zero-lines, we
In minimally twisted bilayer graphene, a moir{e} pattern consisting of AB and BA stacking regions separated by domain walls forms. These domain walls are predicted to support counterpropogating topologically protected helical (TPH) edge states when t
Quasi-periodic moir{e} patterns and their effect on electronic properties of twisted bilayer graphene (TBG) have been intensely studied. At small twist angle $theta$, due to atomic reconstruction, the moire superlattice morphs into a network of narro
We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene (mTBLG). The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerp
A direct signature of electron transport at the metallic surface of a topological insulator is the Aharonov-Bohm oscillation observed in a recent study of Bi_2Se_3 nanowires [Peng et al., Nature Mater. 9, 225 (2010)] where conductance was found to os