Ultra-small-angle graphene twistronics with monolayer spacers: From interlayer hybridisation and moir'e effects to high-temperature magnetotransport oscillations

Based on the analysis of moiré superlattice characteristics and interlayer hybridisation in small-angle twisted graphene multilayers with a monolayer hexagonal boron nitride (hBN) spacer, we predict spectral features and quantum transport effects in these systems. Here, we consider both a twisted bilayer and double bilayers with a spacer, discuss double bilayers in two stacking orders - with and without inversion symmetry - and also compare the results obtained with self-consistent Hartree calculations with and without in-plane periodic charge distribution, offering computationally efficient models for these graphene/hBN/graphene moiré systems. We note parametric intervals where the appearance of minibands can be enhanced by tuning with an out-of-plane displacement field, and identify the miniband edges and van Hove singularities across a broad range of densities and displacement fields. These system host Lifshitz transitions at which the Fermi lines form a network across moiré Brillouin zones, and to which Brown-Zak oscillations converge at low magnetic field and elevated temperatures. We analyse interlayer hybridisation across the same parameter space, discuss how hybridisation affects in-plane magneto-transport in ultra-high-mobility structures, and predict that semiclassical magneto-oscillations of interlayer hybridisation can lead to 1/B-periodic quantum oscillations of resistivity persistent to high temperature.