Concepts of super-valley electron and twist induced quantum super-valley Hall effect

Abstract

Collective motions of electrons in solids are often conveniently described as the movements of quasiparticles. Here we show that these quasiparticles can be hierarchical. Examples are valley electrons, which move in hyperorbits within a honeycomb lattice and forms a valley pseudospin, or the self-rotation of the wave-packet. We demonstrate that twist can induce higher level motions of valley electrons around the moire superlattice of bilayer systems. Such larger scale collective movement of the valley electron, can be regarded as the self-rotation (spin) of a higher-level quasiparticle, or what we call super-valley electron. This quasiparticle, in principle, may have mesoscopic size as the moire supercell can be very large. It could result in fascinating properties like topological and chiral transport, superfluid, etc., even though these properties are absent in the pristine untwisted system. Using twisted antiferromagnetically coupled bilayer with honeycomb lattice as example, we find that there forms a Haldane-like superlattice with periodically staggered magnetic flux and the system could demonstrate quantum super-valley Hall effect. Further analyses reveal that the super-valley electron possesses opposite chirality when projected onto the top and bottom layer, and can be described as two components (magnetic monopoles) of Dirac fermion entangled in real-space, or a giant electron. Our theory opens a new way to understand the collective motions of electrons in solid.