Density of states as a probe of electrostatic confinement in graphene

We theoretically analyze the possibility to confine electrons in single-layer graphene with the help of metallic gates, via the evaluation of the density of states of such a gate-defined quantum dot in the presence of a ring-shaped metallic contact. The possibility to electrostatically confine electrons in a gate-defined ``quantum dot'' with finite-carrier density, surrounded by an undoped graphene sheet, strongly depends on the integrability of the electron dynamics in the quantum dot. With the present calculations we can quantitatively compare confinement in dots with integrable and chaotic dynamics, and verify the prediction that the Berry phase associated with the pseudospin leads to partial confinement in situations where no confinement is expected according to the arguments relying on the classical dynamics only.Comment: 9 pages, 7 figure

Interplay of Aharonov-Bohm and Berry phases in gate-defined graphene quantum dots

We study the influence of a magnetic flux tube on the possibility to electrostatically confine electrons in a graphene quantum dot. Without magnetic flux tube, the graphene pseudospin is responsible for a quantization of the total angular momentum to half-integer values. On the other hand, with a flux tube containing half a flux quantum, the Aharonov-Bohm phase and Berry phase precisely cancel, and we find a state at zero angular momentum that cannot be confined electrostatically. In this case, true bound states only exist in regular geometries for which states without zero-angular-momentum component exist, while non-integrable geometries lack confinement. We support these arguments with a calculation of the two-terminal conductance of a gate-defined graphene quantum dot, which shows resonances for a disc-shaped geometry and for a stadium-shaped geometry without flux tube, but no resonances for a stadium-shaped quantum dot with a $\pi$-flux tube.Comment: 7 pages, 5 figure

Semiclassical theory of the interaction correction to the conductance of antidot arrays

Electron-electron interactions are responsible for a correction to the conductance of a diffusive metal, the "Altshuler-Aronov correction" $\delta G_{AA}$. Here we study the counterpart of this correction for a ballistic conductor, in which the electron motion is governed by chaotic classical dynamics. In the ballistic conductance, the Ehrenfest time $\tau_{E}$ enters as an additional time scale that determines the magnitude of quantum interference effects. The Ehrenfest time effectively poses a short-time threshold for the trajectories contributing to the interaction correction. As a consequence, $\delta G_{AA}$ becomes exponentially suppressed if the Ehrenfest time is larger than the dwell time or the inverse temperature. We discuss the explicit dependence on Ehrenfest time in quasi-one and two-dimensional antidot arrays. For strong interactions, the sign of $\delta G_{AA}$ may change as a function of temperature for temperatures in the vicinity of $\hbar/\tau_{E}$.Comment: 20 pages, 10 figures, published versio

Electronic transport in graphene with particle-hole-asymmetric disorder

We study the conductivity of graphene with a smooth but particle-hole-asymmetric disorder potential. Using perturbation theory for the weak-disorder regime and numerical calculations we investigate how the particle-hole asymmetry shifts the position of the minimal conductivity away from the Dirac point $\varepsilon = 0$. We find that the conductivity minimum is shifted in opposite directions for weak and strong disorder. For large disorder strengths the conductivity minimum appears close to the doping level for which electron and hole doped regions ("puddles") are equal in size

a trajectory-based semiclassical analysis

We review a calculation of the quantum corrections to electrical transport in graphene, using the trajectory-based semiclassical method. Compared to conventional metals, for graphene the semiclassical propagator contains an additional pseudospin structure that influences the results for weak localization, and interaction-induced effects, such as the Altshuler–Aronov correction and dephasing. Our results apply to a sample of graphene that is doped away from the Dirac point and subject to a smooth disorder potential, such that electrons follow classical trajectories. In such a system, the Ehrenfest time enters as an additional timescale

Die Benachteiligung von Kombihilfeempfängern in der kommunalen Arbeitsmarktpolitik

Die Funktion der sozialen Grundsicherung wird in Deutschland durch die Sozialhilfe und die Arbeitslosenhilfe abgedeckt. Während jedoch die Finanzierung der Arbeitslosenhilfe durch den Bund erfolgt, obliegt die Finanzierung der Sozialhilfe den Kommunen. Dieser Dualismus führt mutmaßlich zur Benachteiligung sogenannter Kombihilfeempfänger im Hinblick auf deren Wiedereingliederung in den Arbeitsmarkt durch Maßnahmen der aktiven Arbeitsmarktpolitik. Kombihilfeempfänger sind Personen, deren staatlich garantiertes Mindesteinkommen sowohl aus Sozialhilfe als auch aus Arbeitslosenunterstützung besteht. Ihr Einkommensanspruch ist zwar nicht höher als der von reinen Sozialhilfeempfängern, doch die zwischen Bund und Kommunen geteilte Zuständigkeit für dessen Finanzierung erzeugt Anreize zur gegenseitigen Lastenverschiebung...

A phase‐field based model for coupling two‐phase flow with the motion of immersed rigid bodies

The interaction of immersed rigid bodies with two-phase flow is of high interest in many applications. A model for the coupling of a Hohenberg–Halperin type model for two-phase flow and a fictitious domain method for consideration of rigid bodies is introduced leading to a full multiphase-field method to address the overall problem. A normalized phase variable is used alongside a method for application of wetting boundary conditions over a diffuse fluid-solid interface. This enables the representation of capillary effects and different wetting behavior based on Young\u27s law. A number of simulations is conducted in order to validate the model and highlight its ability to handle a variety of setups for two-phase particulate flow. This includes dynamic wetting situations, the motion of multiple particles within the two-phase flow and the interaction with arbitrarily shaped solid structures inside the domain