Gate-Tunable Magnetism and Giant Magnetoresistance in Suspended Rhombohedral-Stacked Few-Layer Graphene.

Conventionally, magnetism arises from the strong exchange interaction among the magnetic moments of d- or f-shell electrons. It can also emerge in perfect lattices from nonmagnetic elements, such as that exemplified by the Stoner criterion. Here we report tunable magnetism in suspended rhombohedral-stacked few-layer graphene (r-FLG) devices with flat bands. At small doping levels (n ∼ 1011 cm-2), we observe prominent conductance hysteresis and giant magnetoconductance that exceeds 1000% as a function of magnetic fields. Both phenomena are tunable by density and temperature and disappear at n > 1012 cm-2 or T > 5 K. These results are confirmed by first-principles calculations, which indicate the formation of a half-metallic state in doped r-FLG, in which the magnetization is tunable by electric field. Our combined experimental and theoretical work demonstrate that magnetism and spin polarization, arising from the strong electronic interactions in flat bands, emerge in a system composed entirely of carbon atoms.

Ultrasharp Lateral p-n Junctions in Modulation-Doped Graphene.

We demonstrate ultrasharp (≲10 nm) lateral p-n junctions in graphene using electronic transport, scanning tunneling microscopy, and first-principles calculations. The p-n junction lies at the boundary between differentially doped regions of a graphene sheet, where one side is intrinsic and the other is charge-doped by proximity to a flake of α-RuCl3 across a thin insulating barrier. We extract the p-n junction contribution to the device resistance to place bounds on the junction width. We achieve an ultrasharp junction when the boundary between the intrinsic and doped regions is defined by a cleaved crystalline edge of α-RuCl3 located 2 nm from the graphene. Scanning tunneling spectroscopy in heterostructures of graphene, hexagonal boron nitride, and α-RuCl3 shows potential variations on a sub 10 nm length scale. First-principles calculations reveal that the charge-doping of graphene decays sharply over just nanometers from the edge of the α-RuCl3 flake.

Direct Visualization of Native Defects in Graphite and Their Effect on the Electronic Properties of Bernal-Stacked Bilayer Graphene.

Graphite crystals used to prepare graphene-based heterostructures are generally assumed to be defect free. We report here scanning tunneling microscopy results that show graphite commonly used to prepare graphene devices can contain a significant amount of native defects. Extensive scanning of the surface allows us to determine the concentration of native defects to be 6.6 × 108 cm-2. We further study the effects of these native defects on the electronic properties of Bernal-stacked bilayer graphene. We observe gate-dependent intravalley scattering and successfully compare our experimental results to T-matrix-based calculations, revealing a clear carrier density dependence in the distribution of the scattering vectors. We also present a technique for evaluating the spatial distribution of short-scale scattering. Finally, we present a theoretical analysis based on the Boltzmann transport equation that predicts that the dilute native defects identified in our study are an important extrinsic source of scattering, ultimately setting the charge carrier mobility at low temperatures.

Imaging Quantum Interference in Stadium-Shaped Monolayer and Bilayer Graphene Quantum Dots.

Experimental realizations of graphene-based stadium-shaped quantum dots (QDs) have been few and have been incompatible with scanned probe microscopy. Yet, the direct visualization of electronic states within these QDs is crucial for determining the existence of quantum chaos in these systems. We report the fabrication and characterization of electrostatically defined stadium-shaped QDs in heterostructure devices composed of monolayer graphene (MLG) and bilayer graphene (BLG). To realize a stadium-shaped QD, we utilized the tip of a scanning tunneling microscope to charge defects in a supporting hexagonal boron nitride flake. The stadium states visualized are consistent with tight-binding-based simulations but lack clear quantum chaos signatures. The absence of quantum chaos features in MLG-based stadium QDs is attributed to the leaky nature of the confinement potential due to Klein tunneling. In contrast, for BLG-based stadium QDs (which have stronger confinement) quantum chaos is precluded by the smooth confinement potential which reduces interference and mixing between states.

Sublattice Dependence and Gate Tunability of Midgap and Resonant States Induced by Native Dopants in Bernal-Stacked Bilayer Graphene.

The properties of semiconductors can be crucially impacted by midgap states induced by dopants, which can be native or intentionally incorporated in the crystal lattice. For Bernal-stacked bilayer graphene (BLG), which has a tunable band gap, the existence of midgap states induced by dopants or adatoms has been investigated theoretically and observed indirectly in electron transport experiments. Here, we characterize BLG midgap states in real space, with atomic-scale resolution with scanning tunneling microscopy and spectroscopy. We show that the midgap states in BLG-for which we demonstrate gate tunability-appear when the dopant is hosted on the nondimer sublattice sites. We further evidence the presence of narrow resonances at the onset of the high-energy bands (valence or conduction, depending on the dopant type) when the dopants lie on the dimer sublattice sites. Our results are supported by tight-binding calculations that agree remarkably well with the experimental findings.

Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene.

Bloch states of electrons in honeycomb two-dimensional crystals with multivalley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking (ABA TLG), hosts topological magnetic moments with a large and widely tunable valley g factor (g_{ν}), reaching a value g_{ν}∼1050 at the extreme of the studied parametric range. The reported experiment consists in sublattice-resolved scanning tunneling spectroscopy under perpendicular electric and magnetic fields that control the TLG bands. The tunneling spectra agree very well with the results of theoretical modeling that includes the full details of the TLG tight-binding model and accounts for a quantum-dot-like potential profile formed electrostatically under the scanning tunneling microscope tip.

Topological valley transport at bilayer graphene domain walls.

Electron valley, a degree of freedom that is analogous to spin, can lead to novel topological phases in bilayer graphene. A tunable bandgap can be induced in bilayer graphene by an external electric field, and such gapped bilayer graphene is predicted to be a topological insulating phase protected by no-valley mixing symmetry, featuring quantum valley Hall effects and chiral edge states. Observation of such chiral edge states, however, is challenging because inter-valley scattering is induced by atomic-scale defects at real bilayer graphene edges. Recent theoretical work has shown that domain walls between AB- and BA-stacked bilayer graphene can support protected chiral edge states of quantum valley Hall insulators. Here we report an experimental observation of ballistic (that is, with no scattering of electrons) conducting channels at bilayer graphene domain walls. We employ near-field infrared nanometre-scale microscopy (nanoscopy) to image in situ bilayer graphene layer-stacking domain walls on device substrates, and we fabricate dual-gated field effect transistors based on the domain walls. Unlike single-domain bilayer graphene, which shows gapped insulating behaviour under a vertical electrical field, bilayer graphene domain walls feature one-dimensional valley-polarized conducting channels with a ballistic length of about 400 nanometres at 4 kelvin. Such topologically protected one-dimensional chiral states at bilayer graphene domain walls open up opportunities for exploring unique topological phases and valley physics in graphene.

Visualization and Manipulation of Bilayer Graphene Quantum Dots with Broken Rotational Symmetry and Nontrivial Topology.

Electrostatically defined quantum dots (QDs) in Bernal stacked bilayer graphene (BLG) are a promising quantum information platform because of their long spin decoherence times, high sample quality, and tunability. Importantly, the shape of QD states determines the electron energy spectrum, the interactions between electrons, and the coupling of electrons to their environment, all of which are relevant for quantum information processing. Despite its importance, the shape of BLG QD states remains experimentally unexamined. Here we report direct visualization of BLG QD states by using a scanning tunneling microscope. Strikingly, we find these states exhibit a robust broken rotational symmetry. By using a numerical tight-binding model, we determine that the observed broken rotational symmetry can be attributed to low energy anisotropic bands. We then compare confined holes and electrons and demonstrate the influence of BLG's nontrivial band topology. Our study distinguishes BLG QDs from prior QD platforms with trivial band topology.

Visualizing the Effect of an Electrostatic Gate with Angle-Resolved Photoemission Spectroscopy.

Electrostatic gating is pervasive in materials science, yet its effects on the electronic band structure of materials has never been revealed directly by angle-resolved photoemission spectroscopy (ARPES), the technique of choice to noninvasively probe the electronic band structure of a material. By means of a state-of-the-art ARPES setup with submicron spatial resolution, we have investigated a heterostructure composed of Bernal-stacked bilayer graphene (BLG) on hexagonal boron nitride and deposited on a graphite flake. By voltage biasing the latter, the electric field effect is directly visualized on the valence band as well as on the carbon 1s core level of BLG. The band gap opening of BLG submitted to a transverse electric field is discussed and the importance of intra layer screening is put forward. Our results pave the way for new studies that will use momentum-resolved electronic structure information to gain insight on the physics of materials submitted to the electric field effect.

Visualization and Control of Single-Electron Charging in Bilayer Graphene Quantum Dots.

Graphene p-n junctions provide an ideal platform for investigating novel behavior at the boundary between electronics and optics that arise from massless Dirac Fermions, such as whispering gallery modes and Veselago lensing. Bilayer graphene also hosts Dirac Fermions, but they differ from single-layer graphene charge carriers because they are massive, can be gapped by an applied perpendicular electric field, and have very different pseudospin selection rules across a p-n junction. Novel phenomena predicted for these massive Dirac Fermions at p-n junctions include anti-Klein tunneling, oscillatory Zener tunneling, and electron cloaked states. Despite these predictions there has been little experimental focus on the microscopic spatial behavior of massive Dirac Fermions in the presence of p-n junctions. Here we report the experimental manipulation and characterization of massive Dirac Fermions within bilayer graphene quantum dots defined by circular p-n junctions through the use of scanning tunneling microscopy-based (STM) methods. Our p-n junctions are created via a flexible technique that enables realization of exposed quantum dots in bilayer graphene/hBN heterostructures. These quantum dots exhibit sharp spectroscopic resonances that disperse in energy as a function of applied gate voltage. Spatial maps of these features show prominent concentric rings with diameters that can be tuned by an electrostatic gate. This behavior is explained by single-electron charging of localized states that arise from the quantum confinement of massive Dirac Fermions within our exposed bilayer graphene quantum dots.