Bilayer graphene is a unique system where both the Fermi energy and the low-energy electron dispersion can be tuned. This is brought about by an interplay between trigonal warping and the band gap opened by a transverse electric field. Here, we drive the Lifshitz transition in bilayer graphene to experimentally controllable carrier densities by applying a large transverse electric field to a h-BN-encapsulated bilayer graphene structure. We perform magnetotransport measurements and investigate the different degeneracies in the Landau level spectrum. At low magnetic fields, the observation of filling factors -3 and -6 quantum Hall states reflects the existence of three maxima at the top of the valence-band dispersion. At high magnetic fields, all integer quantum Hall states are observed, indicating that deeper in the valence band the constant energy contours are singly connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample. This enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calculated evolution of the Landau level spectrum. The observed evolution of the degeneracies, therefore, reveals the presence of a Lifshitz transition in our system.

Graphene—two-dimensional carbon—is a material with unique mechanical, optical, chemical, and electronic properties. Its use in a wide range of applications was therefore suggested. From an electronic point of view, nanostructured graphene is of great interest due to the potential opening of a band gap, applications in quantum devices, and investigations of physical phenomena. Narrow graphene stripes called “nanoribbons” show clearly different electronical transport properties than micron-sized graphene devices. The conductivity is generally reduced and around the charge neutrality point, the conductance is nearly completely suppressed. While various mechanisms can lead to this observed suppression of conductance, disordered edges resulting in localized charge carriers are likely the main cause in a large number of experiments. Localized charge carriers manifest themselves in transport experiments by the appearance of Coulomb blockade diamonds. This review focuses on the mechanisms responsible for this charge localization, on interpreting the transport details, and on discussing the consequences for physics and applications. Effects such as multiple coupled sites of localized charge, cotunneling processes, and excited states are discussed. Also, different geometries of quantum devices are compared. Finally, an outlook is provided, where open questions are addressed.

We report the experimental observation of Fabry-Pérot interference in the conductance of a gate-defined cavity in a dual-gated bilayer graphene device. The high quality of the bilayer graphene flake, combined with the device's electrical robustness provided by the encapsulation between two hexagonal boron nitride layers, allows us to observe ballistic phase-coherent transport through a 1-μm-long cavity. We confirm the origin of the observed interference pattern by comparing to tight-binding calculations accounting for the gate-tunable band gap. The good agreement between experiment and theory, free of tuning parameters, further verifies that a gap opens in our device. The gap is shown to destroy the perfect reflection for electrons traversing the barrier with normal incidence (anti-Klein tunneling). The broken anti-Klein tunneling implies that the Berry phase, which is found to vary with the gate voltages, is always involved in the Fabry-Pérot oscillations regardless of the magnetic field, in sharp contrast with single-layer graphene. DOI: 10.1103/PhysRevLett.113.116601 PACS numbers: 72.80.Vp, 73.23.-b Interference of particles is a manifestation of the wave nature of matter. A well-known realization is the double-slit experiment, which cannot be described by the laws of Newtonian mechanics, but requires a full quantum description. This experiment has been performed with photons [1,2], electrons [3], and even molecules [4]. Another setting widely used in optics is the Fabry-Pérot (FP) interferometer, where a photon bounces back and forth between two coplanar semitransparent mirrors. Partial waves transmitted after a distinct number of reflections within this cavity interfere and give rise to an oscillatory intensity of the transmitted beam as the mirror separation or the particle energy is varied.In solid-state physics, graphene has proven to be a suitable material for probing electron interference at cryogenic temperatures [5,6]. However, in single-layer graphene (SLG) the realization of FP interferometers is challenging. The absence of a band gap and the Klein tunneling hamper the efficiency of sharp potential steps between the n-and p-type regions, which play the role of the interferometer mirrors [7][8][9]. Theory suggests that smooth barriers enhance the visibility of interference [10,11] due to Klein collimation [12]. Recently, ultraclean suspended SLG devices have shown FP interference with stunning contrast using cavity sizes of more than 1 μm [13][14][15].In bilayer graphene (BLG) potential steps between n-and p-type regions lead to evanescent interface states resulting in a zero-transmission at normal incidence, known as anti-Klein tunneling [7]. Furthermore, in BLG a band gap can be induced by a transverse electric field [16][17][18][19]. The Berry phase of π in SLG has been predicted [20] and observed [10] to cause a phase jump of π in the FP fringes at weak magnetic field (B). In gapless BLG the Berry phase is known to be 2π, but it is yet to be understood how the Berry phase in gapped BLG influ...

We report on the fabrication and electrical characterization of both single layer graphene micronsized devices and nanoribbons on a hexagonal boron nitride substrate. We show that the micronsized devices have significantly higher mobility and lower disorder density compared to devices fabricated on silicon dioxide substrate in agreement with previous findings. The transport characteristics of the reactive-ion-etched graphene nanoribbons on hexagonal boron nitride, however, appear to be very similar to those of ribbons on a silicon dioxide substrate. We perform a detailed study in order to highlight both similarities as well as differences. Our findings suggest that the edges have an important influence on transport in reactive ion-etched graphene nanodevices.

We investigate etched single-layer graphene nanoribbons with different widths ranging from 30 to 130 nm by confocal Raman spectroscopy. We show that the D-line intensity only depends on the edge-region of the nanoribbon and that consequently the fabrication process does not introduce bulk defects. In contrast, the G- and the 2D-lines scale linearly with the irradiated area and therefore with the width of the ribbons. We further give indications that the D- to G-line ratio can be used to gain information about the crystallographic orientation of the underlying graphene. Finally, we perform polarization angle dependent measurements to analyze the nanoribbon edge-regions