Localization physics in graphene moiré superlattices

Since the discovery of graphene, the localization physics has been studied extensively, and both weak antilocalization (WAL) and weak localization (WL) have been observed. A graphene superlattice (GSL) with multiple Dirac cones has emerged as a focus point in condensed-matter physics in recent years. However, the localization physics at multiple Dirac cones has not been studied to date. Here, we study the magnetoconductance in hexagonal boron nitride-graphene moir\'e-superlattice devices. Our magnetoconductance results show a clear signature of WL at the cloned Dirac cone (CDC) over one decade of variation of both carrier concentration and temperature in the two devices. In contrast, the WAL becomes stronger at the primary Dirac cone (PDC) with increasing temperature and lower carrier concentration in one device, in agreement with previous studies, whereas the other device shows stronger WAL for both lower temperature and carrier concentration. Since the observation of WAL at PDC is expected in a cleaner device due to the $\ensuremath{\pi}$ Berry phase, it is natural to ask whether the observation of WL at CDC in our GSL devices has any connection to Berry phase change or not. In order to address this issue we measure the Shubnikov--de Haas (SdH) resistance oscillations, which show a shift of the Berry phase by $\ensuremath{\pi}$ from PDC to CDC, indicating the role of the Berry phase for observing WL at CDC. We further corroborate our results with realistic electronic band structure calculations, which suggest a change in the Fermi surface topology from that with a small Fermi pocket enclosing a single PDC in each valley to a large Fermi surface shared by all the CDCs, in accordance with the change in oscillation frequency from PDC to CDC in the SdH measurements.