Colloquium: Graphene spectroscopy

Spectroscopic studies of electronic phenomena in graphene are reviewed. A variety of methods and techniques are surveyed, from quasiparticle spectroscopies (tunneling, photoemission) to methods probing density and current response (infrared optics, Raman) to scanning probe nanoscopy and ultrafast pump-probe experiments. Vast complimentary information derived from these investigations is shown to highlight unusual properties of Dirac quasiparticles and many-body interaction effects in the physics of graphene.Comment: 36 pages, 16 figure

Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moir\'e Superlattice

Studies on two-dimensional electron systems in a strong magnetic field first revealed the quantum Hall (QH) effect, a topological state of matter featuring a finite Chern number (C) and chiral edge states. Haldane later theorized that Chern insulators with integer QH effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (TLG/hBN) moir\'e superlattice provides an attractive platform to explore Chern insulators because it features nearly flat moir\'e minibands with a valley-dependent electrically tunable Chern number. Here we report the experimental observation of a correlated Chern insulator in a TLG/hBN moir\'e superlattice. We show that reversing the direction of the applied vertical electric field switches TLG/hBN's moir\'e minibands between zero and finite Chern numbers, as revealed by dramatic changes in magneto-transport behavior. For topological hole minibands tuned to have a finite Chern number, we focus on 1/4 filling, corresponding to one hole per moir\'e unit cell. The Hall resistance is well quantized at h/2e2, i.e. C = 2, for |B| > 0.4 T. The correlated Chern insulator is ferromagnetic, exhibiting significant magnetic hysteresis and a large anomalous Hall signal at zero magnetic field. Our discovery of a C = 2 Chern insulator at zero magnetic field should open up exciting opportunities for discovering novel correlated topological states, possibly with novel topological excitations, in nearly flat and topologically nontrivial moir\'e minibands.Comment: 16 pages, 4 figures, and 2 extended figure

Signatures of Gate-Tunable Superconductivity in Trilayer Graphene/Boron Nitride Moir\'e Superlattice

Understanding the mechanism of high temperature (high Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high Tc superconductivity arises from a doped Mott insulator as described by the Hubbard model. 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 ABC-trilayer graphene (TLG) / boron nitride (hBN) moir\'e 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. 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.Comment: 14 pages, 4 figure

Evidence of Gate-Tunable Mott Insulator in Trilayer Graphene-Boron Nitride Moir\'e Superlattice

Mott insulator plays a central role in strongly correlated physics, where the repulsive Coulomb interaction dominates over the electron kinetic energy and leads to insulating states with one electron occupying each unit cell. Doped Mott insulator is often described by the Hubbard model3, which can give rise to other correlated phenomena such as unusual magnetism and even high-temperature superconductivity. A tunable Mott insulator, where the competition between the Coulomb interaction and the kinetic energy can be varied in situ, can provide an invaluable model system for the study of Mott physics. Here we report the realization of such a tunable Mott insulator in the ABC trilayer graphene (TLG) and hexagonal boron nitride (hBN) heterostructure with a moir\'e superlattice. Unlike massless Dirac electrons in monolayer graphene, electrons in pristine ABC TLG are characterized by quartic energy dispersion and large effective mass that are conducive for strongly correlated phenomena. The moir\'e superlattice in TLG/hBN heterostructures leads to narrow electronic minibands that are gate tunable. Each filled miniband contains 4 electrons in one moir\'e lattice site due to the spin and valley degeneracy of graphene. The Mott insulator states emerge at 1/4 and 1/2 fillings, corresponding to one electron and two electrons per site, respectively. Moreover, the Mott states in the ABC TLG/hBN heterostructure exhibit unprecedented tunability: the Mott gap can be modulated in situ by a vertical electrical field, and at the meantime, the electron doping can be gate-tuned to fill the band from one Mott insulating state to another. Our observation of a tunable Mott insulator opens up exciting opportunities to explore novel strongly correlated phenomena in two-dimensional moir\'e superlattice heterostructures.Comment: 11 pages, 4 figure