Hydraulic Jump in One-dimensional Flow

In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic equations. This gives a linear height profile before the jump, as well as a clear dependence of the magnitude of the jump on the outer boundary condition. The importance of viscosity in the jump formation has been convincingly established, and its physical basis has been understood by a time-dependent analysis of the flow equations. In doing so, a very close correspondence has been revealed between a perturbation equation for the flow rate and the metric of an acoustic white hole. We finally provide experimental support for our heuristically developed theory.Comment: 17 Pages, 8 Figures, 1 Table. To appear in European Physical Journal

Resistively-detected NMR lineshapes in a quasi-one dimensional electron system

We observe variation in the resistively-detected nuclear magnetic resonance (RDNMR) lineshapes in quantum Hall breakdown. The breakdown is locally occurred in a gate-defined quantum point contact (QPC) region. Of particular interest is the observation of a dispersive lineshape occured when the bulk 2D electron gas (2DEG) is set to $\nu_{\rm{b}} = 2$ and the QPC filling factor to the vicinity of $\nu_{\rm{QPC}} = 1$, strikingly resemble the dispersive lineshape observed on a 2D quantum Hall state. This previously unobserved lineshape in a QPC points to simultaneous occurrence of two hyperfine-mediated spin flip-flop processes within the QPC. Those events give rise to two different sets of nuclei polarized in the opposite direction and positioned at a separate region with different degree of electronic polarizations.Comment: Accepted as a rapid communication in PR

Delocalized-localized transition in a semiconductor two-dimensional honeycomb lattice

We report the magneto-transport properties of a two-dimensional electron gas in a modulation-doped AlGaAs/GaAs heterostructure subjected to a lateral potential with honeycomb geometry. Periodic oscillations of the magneto-resistance and a delocalized-localized transition are shown by applying a gate voltage. We argue that electrons in such artificial-graphene lattices offer a promising approach for the simulation of quantum phases dictated by Coulomb interactions

Paramagnetic Meissner effect in superconductors from self-consistent solutions of Ginzburg-Landau equations

The paramagnetic Meissner effect (PME) is observed in small superconducting samples, and a number of controversial explanations of this effect are proposed, but there is as yet no clear understanding of its nature. In the present paper PME is considered on the base of the Ginzburg-Landau theory (GL). The one-dimensional solutions are obtained in a model case of a long superconducting cylinder for different cylinder radii R, the GL-parameters \kappa and vorticities m. Acording to GL-theory, PME is caused by the presence of vortices inside the sample. The superconducting current flows around the vortex to screeen the vortex own field from the bulk of the sample. Another current flows at the boundary to screen the external field H from entering the sample. These screening currents flow in opposite directions and contribute with opposite signs to the total magnetic moment (or magnetization) of the sample. Depending on H, the total magnetization M may be either negative (diamagnetism), or positive (paramagnetism). A very complicated saw-like dependence M(H) (and other characteristics), which are obtained on the base of self-consistent solutions of the GL-equations, are discussed.Comment: 6 pages, 5 figures, RevTex, submitted to Phys. Rev.

Dilation of the Giant Vortex State in a Mesoscopic Superconducting Loop

We have experimentally investigated the magnetisation of a mesoscopic aluminum loop at temperatures well below the superconducting transition temperature $T_{c}$. The flux quantisation of the superconducting loop was investigated with a $\mu$-Hall magnetometer in magnetic field intensities between $\pm 100 {Gauss}$. The magnetic field intensity periodicity observed in the magnetization measurements is expected to take integer values of the superconducting flux quanta $\Phi_{0}=h/2e$. A closer inspection of the periodicity, however, reveal a sub flux quantum shift. This fine structure we interpret as a consequence of a so called giant vortex state nucleating towards either the inner or the outer side of the loop. These findings are in agreement with recent theoretical reports.Comment: 12 pages, 5 figures. Accepted for publication in Phys. Rev.

Vortices in Ginzburg-Landau billiards

We present an analysis of the Ginzburg-Landau equations for the description of a two-dimensional superconductor in a bounded domain. Using the properties of a special integrability point of these equations which allows vortex solutions, we obtain a closed expression for the energy of the superconductor. The role of the boundary of the system is to provide a selection mechanism for the number of vortices. A geometrical interpretation of these results is presented and they are applied to the analysis of the magnetization recently measured on small superconducting disks. Problems related to the interaction and nucleation of vortices are discussed.Comment: RevTex, 17 pages, 3 eps figure

Laser-induced disassembly of a graphene single crystal into a nano-crystalline network

We report about investigations of time-dependent structural modifications in single crystal graphene due to laser irradiation even at moderate power levels of 1mW in a diffraction limited spot. The structural modifications have been characterized by in situ scanning confocal Raman spectroscopy, atomic force height microscopy and transport studies. The time evolution of the Raman spectrum reveals two different effects: on a short time scale, dopants, initially present on the flake, are removed. The longer time scale behavior points to a laser induced gradual local decomposition of single crystal graphene into a network of interconnected nano-crystallites with a characteristic length scale of approximately 10 nm due to bond-breaking. The broken bonds offer additional docking sites for adsorbates as confirmed in transport and AFM height studies. These controlled structural modifications may for instance be valuable for enhancing the local reactivity and trimming graphene based gas sensors.Comment: 16 pages, 4 figure

Friedel phases and phases of transmission amplitudes in quantum scattering systems

We illustrate the relation between the scattering phase appearing in the Friedel sum rule and the phase of the transmission amplitude for quantum scatterers connected to two one-dimensional leads. Transmission zero points cause abrupt phase changes $\pm\pi$ of the phase of the transmission amplitude. In contrast the Friedel phase is a continuous function of energy. We investigate these scattering phases for simple scattering problems and illustrate the behavior of these models by following the path of the transmission amplitude in the complex plane as a function of energy. We verify the Friedel sum rule for these models by direct calculation of the scattering phases and by direct calculation of the density of states.Comment: 12 pages, 12 figure