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...

Majorana fermions are zero-energy quasiparticles that may exist in superconducting vortices and interfaces, but their detection is problematic since they have no charge. This is an obstacle to the realization of topological quantum computation, which relies on Majorana fermions to store qubits in a way which is insensitive to decoherence. We show how a pair of neutral Majorana fermions can be converted reversibly into a charged Dirac fermion. These two types of fermions are predicted to exist on the metallic surface of a topological insulator (such as Bi2Se3). Our Dirac-Majorana fermion converter enables electrical detection of a qubit by an interferometric measurement.

We propose a method to probe the nonlocality of a pair of Majorana bound states by crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other (equivalent to the splitting of a Cooper pair). We find that, at sufficiently low excitation energies, this nonlocal scattering process dominates over local Andreev reflection involving a single bound state. As a consequence, the low-temperature and low-frequency fluctuations deltaI(i) of currents into the two bound states i=1, 2 are maximally correlated: deltaI_1deltaI_2[over ]=deltaI_i(2).[over ].

We address the problem of an unscreened Coulomb charge in graphene and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done nonperturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice and (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that cannot be described by the Dirac equation: namely, bound state formation and strong renormalization of the van Hove singularities.

The electronic structure of bilayer graphene is investigated from a resonant Raman study using different laser excitation energies. The values of the parameters of the Slonczewski-Weiss-McClure model for graphite are measured experimentally and some of them differ significantly from those reported previously for graphite, specially that associated with the difference of the effective mass of electrons and holes. The splitting of the two TO phonon branches in bilayer graphene is also obtained from the experimental data. Our results have implications for bilayer graphene electronic devices.