Valley current splitter in minimally twisted bilayer graphene

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 find that (i) the incoming current can be partitioned into both left-right adjacent topological channels and (ii) the forward-propagating current is nonzero. By tuning the Fermi energy from the charge-neutrality point to a band edge, the currents partitioned into the three outgoing channels become nearly equal. Moreover, we find that the current partition node can be designed as a perfect valley filter and energy splitter controlled by electric gating. By changing the relative electric-field magnitude, the intersection of three topological zero lines can transform smoothly into a single zero line, and the current partition can be controlled precisely. We explore the available methods for modulating this device systematically by changing the Fermi energy, the energy gap size, and the size of the central gapless region. The current partition is also influenced by magnetic fields and the system size. Our results provide a microscopic depiction of the electronic transport properties around a unit cell of minimally twisted bilayer graphene and have far-reaching implications in the design of electron-beam splitters and interferometer devices.