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 have realized encapsulated trilayer MoS2 devices with gated graphene contacts. In the bulk, we observe an electron mobility as high as 7000 cm 2 /(V s) at a density of 3 × 10 12 cm −2 at a temperature of 1.9 K. Shubnikov-de Haas oscillations start at magnetic fields as low as 0.9 T. The observed 3-fold Landau level degeneracy can be understood based on the valley Zeeman effect. Negatively biased split gate electrodes allow us to form a channel that can be completely pinched off for sufficiently large gate voltages. The measured conductance displays plateau-like features.Laterally confined two-dimensional (2D) materials offer the opportunity to engineer quantum states with tunable spin, charge and even valley degrees of freedom 1-3 . The pure thinness of these materials in combination with 2D insulators such as boron nitride pave the way for ultrasmall strongly coupled gate-defined quantum devices 4-7 . In addition the variety of transition metal dichalcogenides (TMDCs) materials will allow to choose different strength of spin-orbit interaction that is relevant for electric control of spin and valley-states in view of quantum information processing. In this Letter, we describe a split gate geometry realized on a high-quality molybdenum disulfide (MoS 2 ) van der Waals heterostructure that results in a tunable tunneling barrier, the starting point for any electronic quantum device. The electronic quality of our trilayer MoS 2 device is documented by the observation of Shubnikov-de Haas oscillations (SdHO) occurring at magnetic fields as low as 0.9 T. In addition a 3-fold degeneracy of the Landau levels (LLs) is observed arising from the 3 Q and 3 Q' valleys situated in the middle of the Brillouin zone and shifted in magnetic field by the valley Zeeman effect 8-12 . The constriction can be completely pinched off with resistances values exceeding the quantum of resistance h/e 2 by orders of magnitude, a prerequisite for the realization of any single-electron transistor. We observe the occurrence of plateau-like features in the conductance with a spacing of the order of e 2 /h. These experiments are a first step toward gate controlled quantum devices in transition metal dichalcogenides.To achieve high mobility TMDC devices, we fabricate MoS 2 -based van der Waals heterostructures. As shown schematically in Figure 1a, a trilayer MoS 2 flake (∼ 2 nm thick), contacted with two few-layer graphene (FLG) sheets, is encapsulated between hexagonal boron nitride (hBN) crystals [13][14][15] . The bottom one is 30 nm thick and separates the MoS 2 from substrate phonons and charged impurities, further serving as an atomically flat substrate 16 . The top one is 20 nm thick and prevents the adsorption of organic residues during the fabrication process. To assemble the heterostructure we employ a polymer-based dry pick-up and transfer technique 17,18 using a polycarbonate film 19,20 supported by polydimethylsiloxane. Assembling and exfoliating the various thin films was performed in an argon environment 21 . The films' thickness...
A quantum dot has been etched in bilayer graphene connected by two small constrictions to the leads. We show that this structure does not behave like a single quantum dot but consists of at least three sites of localized charge in series. The high symmetry and electrical stability of the device allowed us to triangulate the positions of the different sites of localized charge and find that one site is located in the island and one in each of the constrictions. Nevertheless we measure many consecutive non-overlapping Coulomb-diamonds in series. In order to describe these findings, we treat the system as a strongly coupled serial triple quantum dot. We find that the non-overlapping Coulomb diamonds arise due to higher order cotunneling through the outer dots located in the constrictions. We extract all relevant capacitances, simulate the measured data with a capacitance model and discuss its implications on electrical transport.
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