Open-orbit induced low field extremely large magnetoresistance in graphene/h-BN superlattices

We report intriguing and hitherto overlooked low-field room temperature extremely large magnetoresistance (XMR) patterns in graphene/hexagonal boron nitride (h-BN) superlattices that emerge due to the existence of open orbits within each miniband. This finding is set against the backdrop of the experimental discovery of the Hofstadter butterfly in moir superlattices, which has sparked considerable interest in the fractal quantum Hall regime. To cope with the challenge of deciphering the low magnetic field dynamics of moir minibands, we utilize a novel semi-classical calculation method, grounded in zero-field Fermi contours, to predict the nontrivial behavior of the Landau-level spectrum. This is compared with fully quantum simulations, enabling an in-depth and contrasted analysis of transport measurements in high-quality graphene-hBN superlattices. Our results not only highlight the primary observation of the open-orbit induced XMR in this system but also shed new light on other intricate phenomena. These include the nuances of single miniband dynamics, evident through Lifshitz transitions, and the complex interplay of semiclassical and quantum effects between these minibands. Specifically, we document transport anomalies linked to trigonal warping, a semiclassical deviation from the expected linear characteristics of Landau levels, and magnetic breakdown phenomena indicative of quantum tunneling, all effects jointly contributing to the intricacies of a rich electronic landscape uncovered at low magnetic fields.