Understanding the mechanism of high temperature (high T c ) superconductivity is a central problem in condensed matter physics. It is often speculated that high T c superconductivity arises from a doped Mott insulator 1 as described by the Hubbard model 2-4 . An exact solution of the Hubbard model, however, is extremely challenging due to the strong electron-electron correlation. Therefore, it is highly desirable to experimentally study a model Hubbard system in which the unconventional superconductivity can be continuously tuned by varying the Hubbard parameters. Here we report signatures of tunable superconductivity in an ABC-trilayer graphene (TLG) / boron nitride (hBN) moiré superlattice. Unlike "magic angle" twisted bilayer graphene, 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 5,6 . Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 kelvin at 1/4 and 1/2 fillings, corresponding to 1 and 2 holes per unit cell, respectively. Upon further cooling, signatures of superconducting domes emerge below 1 kelvin for the electron-and hole-doped sides of the 1/4 filling Mott state. The electronic behavior in the TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron-electron interaction and the miniband bandwidth, which can be tuned continuously with the displacement field D. By simply varying the D field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that TLG/hBN heterostructures offer an attractive model system to explore rich correlated behavior emerging in the tunable triangular Hubbard model.

In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating two-dimensional bulk, without requiring an external magnetic field. Here, we explore the potential of this effect in magnetic topological insulator thin films for metrological applications. Using a cryogenic current comparator system, we measure quantization of the Hall resistance to within one part per million and, at lower current bias, longitudinal resistivity under 10 mΩ at zero magnetic field. Increasing the current density past a critical value leads to a breakdown of the quantized, low-dissipation state, which we attribute to electron heating in bulk current flow. We further investigate the prebreakdown regime by measuring transport dependence on temperature, current, and geometry, and find evidence for bulk dissipation, including thermal activation and possible variable-range hopping.

A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it has been challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb 2 Te 3 films, we were able to reach an extreme quantum limit of the topological surface state and uncover a hidden phase at the zeroth Landau level. First, we discovered an unexpected quantum-Hall-to-insulatortransition near the zeroth Landau level. Then, through a detailed scaling analysis, we found that this quantum-Hall-to-insulator-transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in non-topological systems.A peculiar feature of topologically-protected Dirac surface states in topological insulators (TIs) is the existence of two-fold degenerate zeroth Landau levels (ZLL). [1][2][3] In the presence of structural symmetry (crystal inversion and top/bottom symmetry) and in the absence of tunneling between top and bottom surface states, the ZLL degeneracy is robust and cannot be lifted by the Zeeman energy (indeed they are merely shifted by Zeeman field). [4] Neglecting interactions, increasing the magnetic field such that the filling fraction approaches ! = 0 causes the ZLLs to be half-filled, producing a compressible (metallic) state. This result holds even in the presence of non-magnetic random disorder which on average preserves the structural symmetry. In contrast, conventional two-dimensional electron gases (2DEGs) are insulating near ! = 0, i.e., near the bottom of the lowest LL, due to the presence of localized states at the tail of the lowest LL.Studying the physics of ZLL in TIs requires the Fermi level (E F ) to be close to the Dirac point. Access to this regime has proven challenging because high defect densities in TI systems push E F away from the Dirac point and also introduce significant level of electron-hole puddles