No abstract

We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magneto-transport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to mid-infrared energies by using fields of < ∼ 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.PACS numbers: 81.05. Uw, 73.20.At, 73.21.Ac, The electronic structure of materials is given by their chemical composition and specific arrangements of atoms in a crystal lattice and, accordingly, can be changed only slightly by external factors such as temperature or high pressure. In this Letter we show, both experimentally and theoretically, that the band structure of bilayer graphene can be controlled by an applied electric field so that the electronic gap between the valence and conduction bands can be tuned between zero and mid-infrared energies. This makes bilayer graphene the only known semiconductor with a tunable energy gap and may open the way for developing photodetectors and lasers tunable by the electric field effect. The development of a graphene-based tunable semiconductor being reported here, as well as the discovery of anomalous integer quantum Hall effects (QHE) in single layer [1,2] and unbiased bilayer [3] graphene, which are associated with massless [4] and massive [5] Dirac fermions, respectively, demonstrate the potential of these systems for carbonbased electronics [6]. Furthermore, the deep connection between the electronic properties of graphene and certain theories in particle physics makes graphene a test bed for many ideas in basic science.Below we report the experimental realization of a tunable-gap graphene bilayer and provide its theoretical description in terms of a tight-binding model corrected by charging effects (Hartree approach) [7]. Our main findings are as follows: (i) in a magnetic field, a pronounced plateau at zero Hall conductivity σ xy = 0 is found for the biased bilayer, which is absent in the unbiased case and can only be understood as due to the opening of a sizable gap, ∆ g , between the valence and conductance bands; (ii) the cyclotron mass, m c , in the bilayer biased by chemical doping is an asymmetric function of carrier density, n, which provides a clear signature of a gap and allows its estimate; (iii) by comparing the observed behavior with our tight-binding results, we show that the gap can be tuned to values larger than 0.2 eV; (iv) we have crosschecked our theory against angle-resolved photoemission spectroscopy (ARPES) data [8] and found excellent agreement.The devices used in our experiments were made from bilayer graphene prepared by micromechanical cleavage of graphite on top of an oxidized silicon wafer (300 nm of SiO 2 ) [9]. By using electron-beam lithography, the graphene samples were then processed into Hall bar devices similar to those repor...

Electronic instabilities at the crossing of the Fermi energy with a Van Hove singularity in the density of states often lead to new phases of matter such as superconductivity, magnetism or density waves. However, in most materials this condition is difficult to control. In the case of single-layer graphene, the singularity is too far from the Fermi energy and hence difficult to reach with standard doping and gating techniques. Here we report the observation of low-energy Van Hove singularities in twisted graphene layers seen as two pronounced peaks in the density of states measured by scanning tunneling spectroscopy. We demonstrate that a rotation between stacked graphene layers can generate Van Hove singularities, which can be brought arbitrarily close to the Fermi energy by varying the angle of rotation. This opens intriguing prospects for Van Hove singularity engineering of electronic phases.Comment: 21 pages 5 figure

The continuum model of the twisted graphene bilayer [Lopes dos Santos, Peres, and Castro Neto, Phys. Rev. Lett. 99, 256802 (2007)] is extended to include all types of commensurate structures. The essential ingredient of the model, the Fourier components of the spatially modulated hopping amplitudes, can be calculated analytically for any type of commensurate structures in the low-twist-angle limit. We show that the Fourier components that could give rise to a gap in the sublattice exchange symmetric (SE-even) structures discussed by Mele [Phys. Rev. B 81, 161405 (2010)] vanish linearly with angle, whereas the amplitudes that saturate to finite values, as θ → 0, ensure that all low-angle structures share essentially the same physics. We extend our previous calculations beyond the validity of perturbation theory to discuss the disappearance of Dirac cone structure at angles below θ 1 • .

We present a study of different models of local disorder in graphene. Our focus is on the main effects that vacancies -random, compensated and uncompensated -, local impurities and substitutional impurities bring into the electronic structure of graphene. By exploring these types of disorder and their connections, we show that they introduce dramatic changes in the low energy spectrum of graphene, viz. localized zero modes, strong resonances, gap and pseudogap behavior, and non-dispersive midgap zero modes.