Correlations in moiré heterostructures
Keywords: Applied Physics.

Moiré patterns in van der Waals heterostructures are a readily realizable class of 2D superlattices with electronic properties distinct from those of the parent materials that can be controlled by the composition and relative orientations of layers. The large artificial superlattice generates minibands that disperse on a finer energy scale in a significantly smaller mini Brillouin zone. I begin with transport measurements in highly aligned graphene/hexagonal boron nitride (hBN) heterostructures, a high electron mobility superlattice with miniband edges and Van Hove singularities that are accessible via electrostatic gating. By using recently developed absorptive pinhole collimators, consisting of absorptive sidewalls between a pair of collinear slits, it is possible to populate and detect a narrow window of $-states. Low-field transport measurements yield results consistent with ballistic Monte Carlo simulations based on numerical bandstructure calculations when the superlattice has been tuned to exhibit non-circular Fermi surfaces. Subsequent scanning gate measurements spatially image the non-circular Fermi surface, raising the possibility of using absorptive pinhole collimators as geometric valley filters. A number of moiré superlattices have recently emerged that exhibit flat electronic bands, making them ideal for exploring strongly correlated physics. The flat bands in magic-angle twisted bilayer graphene (tBLG) and ABC-trilayer graphene aligned with hBN (ABC-TLG/hBN) have been shown to give rise to correlated insulators [1,2]. An amazing recent discovery is that tBLG becomes superconducting when doped slightly away from two holes per site, reminiscent of high temperature superconductors [3]. Understanding the mechanism of high-transition-temperature (high-$T_c$) superconductivity is a central problem in condensed matter physics. It is highly desirable to study a tunable Hubbard system, in which systematic investigations of the unconventional superconductivity and its evolution with the Hubbard parameters can deepen our understanding of high-$T_c$ superconductivity. I begin with a report of signatures of tunable superconductivity in ABC-TLG/hBN. Unlike in tBLG, theoretical calculations show that under a vertical displacement field, the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice [2,4]. Signatures of superconductivity emerge below 1 kelvin for the electron- and hole-doped sides of the one-quarter-filling correlated state. The electronic behaviour in the ABC-TLG/hBN superlattice is expected to depend sensitively on the interplay between electron--electron interactions and the miniband bandwidth. By varying the vertical displacement field, transitions from the candidate superconductor to correlated insulator and metallic phases are observed. Superconductivity is one of many possible ground states in flat band systems when electron-electron interactions dominate. I present evidence of an incipient Chern insulating state at integer filling of the flat band in both tBLG and ABC-TLG/hBN. Notably, in tBLG, the magnetization of the sample can be reversed by applying a small direct current. Additionally, when tilting a tBLG sample in an external magnetic field, the ferromagnetism is highly anisotropic. Because spin-orbit coupling is negligible in graphene [5], such behavior is unlikely to come from spin, but rather favors theories in which the ferromagnetism is orbital. For an in-plane field larger than