The focusing of electric current by a single p-n junction in graphene is theoretically predicted. Precise focusing may be achieved by fine-tuning the densities of carriers on the n- and p-sides of the junction to equal values. This finding may be useful for the engineering of electronic lenses and focused beam splitters using gate-controlled n-p-n junctions in graphene-based transistors.

We show that an electrostatically created n-p junction separating the electron and hole gas regions in a graphene monolayer transmits only those quasiparticles that approach it almost perpendicularly to the n-p interface. Such a selective transmission of carriers by a single n-p junction would manifest itself in non-local magnetoresistance effect in arrays of such junctions and determines the unusual Fano factor in the current noise universal for the n-p junctions in graphene.

Disordered conductors with resistivity above the resistance quantum h/e 2 should exhibit an insulating behaviour at low temperatures, a universal phenomenon known as a strong (Anderson) localization [1][2][3] . Observed in a multitude of materials, including damaged graphene and its disordered chemical derivatives [4][5][6][7][8][9][10] , Anderson localization has not been seen in generic graphene, despite its resistivity near the neutrality point reaching ≈h/e 2 per carrier type 4,5 . It has remained a puzzle why graphene is such an exception. Here we report a strong localization and the corresponding metal-insulator transition in ultra-high-quality graphene. The transition is controlled externally, by changing the carrier density in another graphene layer placed at a distance of several nm and decoupled electrically. The entire behaviour is explained by electron-hole puddles that disallow localization in standard devices but can be screened out in doublelayer graphene. The localization that occurs with decreasing rather than increasing disorder is a unique occurrence, and the reported double-layer heterostructures presents a new experimental system that invites further studies.Resistivity values ≈h/e 2 indicate that the electron mean free path l is shorter than the Fermi wavelength λ F , so that quantum interference becomes a dominant feature in electron diffusion, leading to Anderson localization in the absence of phase-breaking processes at low temperatures (T ). The scope of this phenomenon extends beyond electronic systems-into optical and acoustic phenomena as well 1-3 -but not generic graphene, which remains metallic at liquid-helium T (refs 4,5) and exhibits only a weak T dependence that can be explained by phonons and thermally excited carriers 11 . Earlier theoretical studies have suggested that Dirac electrons can evade localization for certain types of disorder 3,12-15 , with the extreme example being graphene subjected to a smooth Coulomb potential 16,17 . However, for generic disorder that involves scattering between the two graphene valleys, the localization is expected to be unavoidable 3,18,19 . Experiments do not show this. In this Letter, we describe a double-layer electronic system made of two closely-spaced but electrically isolated graphene monolayers sandwiched in boron nitride. In the following, the two layers in the double layer graphene (DLG) heterostructure are referred to as the studied and control layers. At low doping n C in the control layer, the studied layer exhibits the standard behaviour with a minimum metallic conductivity of ∼4e 2 /h. However, for n C > 10 11 cm −2 , the resistivity ρ of the studied layer diverges near the neutrality point (NP) at T < 70 K. This divergence can be suppressed by a small perpendicular field B < 0.1 T, which indicates that this is an interference effect rather than a gap opening. We attribute the metal-insulator transition (MIT) to the recovery of an intrinsic behaviour such that graphene exhibits Anderson localization if its ρ reaches values o...

We show that Friedel oscillations (FO) in grapehene are strongly affected by the chirality of electrons in this material. In particular, the FO of the charge density around an impurity show a faster, δρ ∼ r −3 , decay than in conventional 2D electron systems and do not contribute to a linear temperature-dependent correction to the resistivity. In contrast, the FO of the exchange field which surrounds atomically sharp defects breaking the hexagonal symmetry of the honeycomb lattice lead to a negative linear T-dependence of the resistivity. Screening strongly influences properties of impurities in metals and semiconductors. While Thomas-Fermi screening suppresses the long-range tail of a charged impurity potential, Friedel oscillations (FO) of the electron density around a defect [1] are felt by scattered electrons at a distance much longer than the Thomas-Fermi screening length. Friedel oscillations originate from the singular behavior of the response function of the Fermi liquid at wave vector 2k F . At zero temperature the decay of the amplitude δρ of these oscillations with distance r from the impurity obeys a power law dependence. In a nonrelativistic degenerate two-dimensional (2D) Fermi gas [2], δρ ∝ cos(2k F r + δ)/r 2 . In 2D electron systems Bragg scattering off the potential created by these long-range FO strongly renormalises the momentum relaxation rate, τ −1 for quasi-particles near the Fermi level, ǫ ≈ ǫ F , which leads to a linear temperature dependence of the resistivity [3, 4, 5, 6] in a 'ballistic' temperature range ǫ F > T > h/τ confirmed in recent experiments on semiconductor heterostructures and Si field-effect transistors [7].Graphene-based transistor [8,9] is a recent invention which attracts a lot of attention. Improvement of the performance of this device requires identification of the dominant source of electron scattering limiting its mobility. Those can be structural defects of graphene lattice (vacancies and dislocations), substitutional disorder, chemical deposits on graphene and, importantly, charges trapped in or on the surface of the underlying substrate.In this Letter we investigate the effects of screening of scatterers in graphene, and show how the phenomenon of FO can be used to gain insight into the microscopic nature of disorder. Graphene (a monolayer of graphite) is a gapless 2D semiconductor with a Dirac-like dispersion of carriers [10,11]. In this material, it is the Thomas-Fermi screening which is responsible [12] for the experimentally observed linear dependence of graphene conductivity on the carrier density [8,9]. Moreover, quasiparticles in graphene possess chiral properties related to the sublattice composition of the electron wave on a 2D honeycomb lattice [10]. Below we show that, due to the latter peculiarity of graphene, FO of the electron density decay as δρ ∼ r −3 at a long distance from an impurity [faster than in a usual 2D metal] and the linear temperaturedependent correction to the resistivity,