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.

We study the transport properties of graphene nanoribbons of standardized 30 nm width and varying lengths. We find that the extent of the gap observed in transport as a function of Fermi energy in these ribbons (the "transport gap") does not have a strong dependence on ribbon length, while the extent of the gap as a function of source-drain voltage (the "source-drain gap") increases with increasing ribbon length. We anneal the ribbons to reduce the amplitude of the disorder potential, and find that the transport gap both shrinks and moves closer to zero gate voltage. In contrast, annealing does not systematically affect the source-drain gap. We conclude that the transport gap reflects the overall strength of the background disorder potential, while the source-drain gap is sensitively dependent on its details. Our results support the model that transport in graphene nanoribbons occurs through quantum dots forming along the ribbon due to a disorder potential induced by charged impurities.Comment: 10 pages, 8 figure

Rational design of long-period artificial lattices yields effects unavailable in simple solids. The moiré pattern in highly aligned graphene/hexagonal boron nitride (h-BN) heterostructures is a lateral superlattice with high electron mobility and an unusual electronic dispersion whose miniband edges and saddle points can be reached by electrostatic gating. We investigated the dynamics of electrons in moiré minibands by measuring ballistic transport between adjacent local contacts in a magnetic field, known as the transverse electron focusing effect. At low temperatures, we observed caustics of skipping orbits extending over hundreds of superlattice periods, reversals of the cyclotron revolution for successive minibands, and breakdown of cyclotron motion near van Hove singularities. At high temperatures, electron-electron collisions suppress focusing. Probing such miniband conduction properties is a necessity for engineering novel transport behaviors in superlattice devices.

A simple surface band structure and a large bulk band gap have allowed Bi2Se3 to become a reference material for the newly discovered three-dimensional topological insulators, which exhibit topologically protected conducting surface states that reside inside the bulk band gap. Studying topological insulators such as Bi2Se3 in nanostructures is advantageous because of the high surface-to-volume ratio, which enhances effects from the surface states; recently reported Aharonov-Bohm oscillation in topological insulator nanoribbons by some of us is a good example. Theoretically, introducing magnetic impurities in topological insulators is predicted to open a small gap in the surface states by breaking time-reversal symmetry. Here, we present synthesis of magnetically doped Bi2Se3 nanoribbons by vapor-liquid-solid growth using magnetic metal thin films as catalysts. Although the doping concentration is less than approximately 2%, low-temperature transport measurements of the Fe-doped Bi2Se3 nanoribbon devices show a clear Kondo effect at temperatures below 30 K, confirming the presence of magnetic impurities in the Bi2Se3 nanoribbons. The capability to dope topological insulator nanostructures magnetically opens up exciting opportunities for spintronics.