Coulomb drag between one-dimensional conductors

We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length $L$ attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in the conductors acquire energy gap $M$. At energies larger than $\Gamma = const \times v_- \exp (-LM/v_-)/L + \Gamma_{+}$, where $\Gamma_{+}$ is the impurity scattering rate, and for $L>v_-/M$, where $v_-$ is the fluctuation velocity, the gap leads to an ``ideal'' drag with almost equal currents in the conductors. At low energies the drag is suppressed by coherent instanton tunneling, and the zero-temperature transconductance vanishes, indicating the Fermi liquid behavior.Comment: 5 twocolumn pages in RevTex, added 1 eps-Figure and calculation of trans-resistanc

Scaling of the quantum-Hall plateau-plateau transition in graphene

The temperature dependence of the magneto-conductivity in graphene shows that the widths of the longitudinal conductivity peaks, for the N=1 Landau level of electrons and holes, display a power-law behavior following $\Delta \nu \propto T^{\kappa}$ with a scaling exponent $\kappa = 0.37\pm0.05$. Similarly the maximum derivative of the quantum Hall plateau transitions $(d\sigma_{xy}/d\nu)^{max}$ scales as $T^{-\kappa}$ with a scaling exponent $\kappa = 0.41\pm0.04$ for both the first and second electron and hole Landau level. These results confirm the universality of a critical scaling exponent. In the zeroth Landau level, however, the width and derivative are essentially temperature independent, which we explain by a temperature independent intrinsic length that obscures the expected universal scaling behavior of the zeroth Landau level

Density of states and zero Landau level probed through capacitance of graphene

We report capacitors in which a finite electronic compressibility of graphene dominates the electrostatics, resulting in pronounced changes in capacitance as a function of magnetic field and carrier concentration. The capacitance measurements have allowed us to accurately map the density of states D, and compare it against theoretical predictions. Landau oscillations in D are robust and zero Landau level (LL) can easily be seen at room temperature in moderate fields. The broadening of LLs is strongly affected by charge inhomogeneity that leads to zero LL being broader than other levels

Gap opening in the zeroth Landau level of graphene

We have measured a strong increase of the low-temperature resistivity $\rho_{xx}$ and a zero-value plateau in the Hall conductivity $\sigma_{xy}$ at the charge neutrality point in graphene subjected to high magnetic fields up to 30 T. We explain our results by a simple model involving a field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements. The model reproduces both the increase in $\rho_{xx}$ and the anomalous $\nu=0$ plateau in $\sigma_{xy}$ in terms of coexisting electrons and holes in the same spin-split zero-energy Landau level.Comment: 4 pages, 3 figure

Fractional charge in transport through a 1D correlated insulator of finite length

Transport through a one channel wire of length $L$ confined between two leads is examined when the 1D electron system has an energy gap $2M$: $M > T_L \equiv v_c/L$ induced by the interaction in charge mode ($v_c$: charge velocity in the wire). In spinless case the transformation of the leads electrons into the charge density wave solitons of fractional charge $q$ entails a non-trivial low energy crossover from the Fermi liquid behavior below the crossover energy $T_x \propto \sqrt{T_L M} e^{-M /[T_L(1-q^2)]}$ to the insulator one with the fractional charge in current vs. voltage, conductance vs. temperature, and in shot noise. Similar behavior is predicted for the Mott insulator of filling factor $\nu = integer/(2 m')$.Comment: 5 twocolumn pages in RevTex, no figure

The mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean--field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-like dynamo. In view of this application the second--order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $\alpha$--effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.Comment: 16 pages, 2 figures, in PRE pres

Atomically thin boron nitride: a tunnelling barrier for graphene devices

We investigate the electronic properties of heterostructures based on ultrathin hexagonal boron nitride (h-BN) crystalline layers sandwiched between two layers of graphene as well as other conducting materials (graphite, gold). The tunnel conductance depends exponentially on the number of h-BN atomic layers, down to a monolayer thickness. Exponential behaviour of I-V characteristics for graphene/BN/graphene and graphite/BN/graphite devices is determined mainly by the changes in the density of states with bias voltage in the electrodes. Conductive atomic force microscopy scans across h-BN terraces of different thickness reveal a high level of uniformity in the tunnel current. Our results demonstrate that atomically thin h-BN acts as a defect-free dielectric with a high breakdown field; it offers great potential for applications in tunnel devices and in field-effect transistors with a high carrier density in the conducting channel.Comment: 7 pages, 5 figure

Negative local resistance caused by viscous electron backflow in graphene

Graphene hosts a unique electron system in which electron-phonon scattering is extremely weak but electron-electron collisions are sufficiently frequent to provide local equilibrium above liquid nitrogen temperature. Under these conditions, electrons can behave as a viscous liquid and exhibit hydrodynamic phenomena similar to classical liquids. Here we report strong evidence for this transport regime. We find that doped graphene exhibits an anomalous (negative) voltage drop near current injection contacts, which is attributed to the formation of submicrometer-size whirlpools in the electron flow. The viscosity of graphene's electron liquid is found to be ~0.1 m$^2$ /s, an order of magnitude larger than that of honey, in agreement with many-body theory. Our work shows a possibility to study electron hydrodynamics using high quality graphene

Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise

The inhomogeneous Tomonaga Luttinger liquid model describing an interacting quantum wire adiabatically coupled to non-interacting leads is analyzed in the presence of a weak impurity within the wire. Due to strong electronic correlations in the wire, the effects of impurity backscattering, finite bias, finite temperature, and finite length lead to characteristic non-monotonic parameter dependencies of the average current. We discuss oscillations of the non-linear current voltage characteristics that arise due to reflections of plasmon modes at the impurity and quasi Andreev reflections at the contacts, and show how these oscillations are washed out by decoherence at finite temperature. Furthermore, the finite frequency current noise is investigated in detail. We find that the effective charge extracted in the shot noise regime in the weak backscattering limit decisively depends on the noise frequency $\omega$ relative to $v_F/gL$, where $v_F$ is the Fermi velocity, $g$ the Tomonaga Luttinger interaction parameter, and $L$ the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is non-vanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.Comment: 28 pages, 19 figures, published version with minor change