Quantum Transport and Fractional Hall Effect in Moiré Correlated/Anticorrelated Channels

Twisted bilayer graphene (tBLG) including interlayer interaction and rotational disorder shows anomalous electronic transport as a function of twist-angles (tAs). Quantum criticality of metal-insulator transitions of twisted nanostructures has been recently discovered and characterized by their transport measurement [1]. In this work, we address a new perspective of hybridization of fermions in twisted graphene nanoribbons (tGN) by representing a physical map of electronic properties and electronic transport of circular (with anticorrelated surfaces) and rectangular (with correlated surfaces) twisted tGN channels for two regimes of small and large tAs. Analysis of band structure reveals a phase transition of metal to semiconductor occurs in rectangular (correlated) case, sweeping small tAs to large ones. Local flat bands at the AA stacking of small and magic angles of circular (anticorrelated) twisted nanoribbons are formed by effective hybridization of local fermion momenta as f-orbitals and itinerant conduction electrons as c-orbitals, while electrons of extended topological conduction bands are responsible for transport and delocalization. This implies a different transport mechanism; where he energy resolved transmission of circular (anticorrelated) channels reveals pseudo-band and pseudo-gap depending on tAs. Moreover, rectangular channels with correlated surfaces indicate more electronic transmission than anticorrelated counterparts with wider pseudo-bands. Furthermore, the hybridization of f- and c- orbitals create the fractional Hall conductivity of circular (anticorrelated) tGNs. This study probes exotic quantum states in twisted van der Waals (vdW) homostructure with correlated/anticorrelated interfaces, engineering the quantum transport of twisted nanoribbons as building blocks for future quantum circuits and Hall sensors.