We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity σ is equal to the ballistic value 4e2/πh for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with σ≃4×0.4e2/h at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is also obtained at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.

We demonstrate that the Bell test cannot be realized at finite temperatures in the vast majority of electronic setups proposed previously for quantum entanglement generation. This fundamental difficulty is shown to originate in a finite probability of quasiparticle emission from Fermi-sea detectors. In order to overcome the feedback problem we suggest a detection strategy, which takes advantage of a resonant coupling to the quasiparticle drains. Unlike other proposals the designed Bell test provides a possibility to determine the critical temperature for entanglement production in the solid state.

A theoretical model is proposed to describe asymmetric gate-voltage dependence of conductance and noise in two-terminal ballistic graphene devices. The model is analyzed independently within the self-consistent Hartree and Thomas-Fermi approximations. Our results justify the prominent role of metal contacts in recent experiments with suspended graphene flakes. The contact-induced electrostatic potentials in graphene demonstrate a power-law decay with the exponent varying from -1 to -0.5. Within our model we explain electron-hole asymmetry and strong Fabri-Perot oscillations of the conductance and noise at positive doping, which were observed in many experiments with submicrometer samples. Limitations of the Thomas-Fermi approximation in a vicinity of the Dirac point are discussed.Comment: 7 pages, 8 figure

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