On the possibility of a warped disc origin of the inclined stellar discs at the Galactic Centre

(Abridged) The Galactic Center (GC) hosts a population of young stars some of which seem to form mutually inclined discs of clockwise and counter clockwise rotating stars. We present a warped disc origin scenario for these stars assuming that an initially flat accretion disc becomes warped due to the Pringle instability, or due to Bardeen-Petterson effect, before it fragments to stars. We show that this is plausible if the star formation efficiency $\epsilon_{SF} \lesssim 1$, and the viscosity parameter $\alpha \sim 0.1$. After fragmentation, we model the disc as a collection of concentric, circular, mutually tilted rings, and construct warped disc models for mass ratios and other parameters relevant to the GC environment, but also for more massive discs. We take into account the disc's self-gravity and the torques exerted by a surrounding star cluster. We show that a self-gravitating low-mass disc ($M_d / M_{bh} \sim 0.001$) precesses in integrity in the life-time of the stars, but precesses freely when the torques from a non-spherical cluster are included. An intermediate-mass disc ($M_d / M_{bh} \sim 0.01$) breaks into pieces which precess independently in the self-gravity-only case, and become disrupted in the presence of the star cluster torques. For a high-mass disc ($M_d / M_{bh} \sim 0.1$) the evolution is dominated by self-gravity and the disc is broken but not dissolved. The time-scale after which the disc breaks scales almost linearly with ($M_d / M_{bh}$) for self-gravitating models. Typical values are longer than the age of the stars for a low mass disc, and are in the range $\sim 8 \times 10^4-10^5$ yr for high and intermediate-mass discs respectively. None of these models explain the rotation properties of the two GC discs, but a comparison of them with the clockwise disc shows that the lowest mass model in a spherical star cluster matches the data best.Comment: 16 pages, 19 figures, abstract abridged to meet arXiv requirements. Accepted for publication in MNRA

Stability of spin droplets in realistic quantum Hall devices

We study the formation and characteristics of "spin droplets",i.e., compact spin-polarized configurations in the highest occupied Landau level, in an etched quantum Hall device at filling factors $2\leq\nu\leq3$. The confining potential for electrons is obtained with self-consistent electrostatic calculations on a GaAs/AlGaAs heterostructure with experimental system parameters. Real-space spin-density-functional calculations for electrons confined in the obtained potential show the appearance of stable spin droplets at $\nu\sim 5/2$. The qualitative features of the spin droplet are similar to those in idealized (parabolic) quantum-dot systems. The universal stability of the state against geometric deformations underline the applicability of spin droplets in, e.g., spin-transport through quantum point contacts.Comment: 11 pages, 6 figure

Realistic modelling of quantum point contacts subject to high magnetic fields and with current bias at out of linear response regime

The electron and current density distributions in the close proximity of quantum point contacts (QPCs) are investigated. A three dimensional Poisson equation is solved self-consistently to obtain the electron density and potential profile in the absence of an external magnetic field for gate and etching defined devices. We observe the surface charges and their apparent effect on the confinement potential, when considering the (deeply) etched QPCs. In the presence of an external magnetic field, we investigate the formation of the incompressible strips and their influence on the current distribution both in the linear response and out of linear response regime. A spatial asymmetry of the current carrying incompressible strips, induced by the large source drain voltages, is reported for such devices in the non-linear regime.Comment: 16 Pages, 9 Figures, submitted to PR

Self-consistent Coulomb picture of an electron-electron bilayer system

In this work we implement the self-consistent Thomas-Fermi approach and a local conductivity model to an electron-electron bilayer system. The presence of an incompressible strip, originating from screening calculations at the top (or bottom) layer is considered as a source of an external potential fluctuation to the bottom (or top) layer. This essentially yields modifications to both screening properties and the magneto-transport quantities. The effect of the temperature, inter-layer distance and density mismatch on the density and the potential fluctuations are investigated. It is observed that the existence of the incompressible strips plays an important role simply due to their poor screening properties on both screening and the magneto-resistance (MR) properties. Here we also report and interpret the observed MR Hysteresis within our model.Comment: 12 pages, 12 figures, submitted to PR

Interaction mediated asymmetries of the quantized Hall effect

Experimental and theoretical investigations on the integer quantized Hall effect in gate defined narrow Hall bars are presented. At low electron mobility the classical (high temperature) Hall resistance line RH(B) cuts through the center of all Hall plateaus. In contrast, for our high mobility samples the intersection point, at even filling factors \nu = 2; 4 ..., is clearly shifted towards larger magnetic fields B. This asymmetry is in good agreement with predictions of the screening theory, i. e. taking Coulomb interaction into account. The observed effect is directly related to the formation of incompressible strips in the Hall bar. The spin-split plateau at \nu= 1 is found to be almost symmetric regardless of the mobility. We explain this within the so-called effective g-model.Comment: 4 pages, 3 figure

Exchange-correlation enhancement of the Lande-g* factor in integer quantized Hall plateaus

We study the emergent role of many-body effects on a two dimensional electron gas (2DEG) within the Thomas-Fermi-Poisson approximation, including both the exchange and correlation interactions in the presence of a strong perpendicular magnetic field. It is shown that, the indirect interactions widen the odd-integer incompressible strips spatially, whereas the even-integer filling factors almost remain unaffected.Comment: 8 pages,4 figure

Incompressible strips in dissipative Hall bars as origin of quantized Hall plateaus

We study the current and charge distribution in a two dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasi-local transport model, that includes non-linear screening effects on the conductivity via the self-consistently calculated density profile. The existence of ``incompressible strips'' with integer Landau level filling factor is investigated within a Hartree-type approximation, and non-local effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the longitudinal resistance as continuous functions of the magnetic field B, with plateaus of finite widths and the well-known, exactly quantized values. We emphasize the close relation between these plateaus and the existence of incompressible strips, and we show that for B values within these plateaus the potential variation across the Hall bar is very different from that for B values between adjacent plateaus, in agreement with recent experiments.Comment: 13 pages, 11 figures, All color onlin

Simulations of Direct Collisions of Gas Clouds with the Central Black Hole

We perform numerical simulations of clouds in the Galactic Centre (GC) engulfing the nuclear super-massive black hole and show that this mechanism leads to the formation of gaseous accretion discs with properties that are similar to the expected gaseous progenitor discs that fragmented into the observed stellar disc in the GC. As soon as the cloud hits the black hole, gas with opposite angular momentum relative to the black hole collides downstream. This process leads to redistribution of angular momentum and dissipation of kinetic energy, resulting in a compact gaseous accretion disc. A parameter study using thirteen high resolution simulations of homogeneous clouds falling onto the black hole and engulfing it in parts demonstrates that this mechanism is able to produce gaseous accretion discs that could potentially be the progenitor of the observed stellar disc in the GC. A comparison of simulations with different equations of state (adiabatic, isothermal and full cooling) demonstrates the importance of including a detailed thermodynamical description. However the simple isothermal approach already yields good results on the radial mass transfer and accretion rates, as well as disc eccentricities and sizes. We find that the cloud impact parameter strongly influences the accretion rate whereas the impact velocity has a small affect on the accretion rate.Comment: 21 pages, 18 figures, Accepted for publication in MNRA

Quantum Hall effect in a high-mobility two-dimensional electron gas on the surface of a cylinder

The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous current-density distribution gives rise to additional features in the magneto-transport, such as resistance asymmetry and modified longitudinal resistances. We experimentally demonstrate that the asymmetry relations satisfied in the integer filling factor regime are valid also in the transition regime to non-integer filling factors, thereby suggesting a more general form of these asymmetry relations. A model is developed based on the screening theory of the integer quantum Hall effect that allows the self-consistent calculation of the local electron density and thereby the local current density including the current along incompressible stripes. The model, which also includes the so-called `static skin effect' to account for the current density distribution in the compressible regions, is capable of explaining the main experimental observations. Due to the existence of an incompressible-compressible transition in the bulk, the system behaves always metal-like in contrast to the conventional Landauer-Buettiker description, in which the bulk remains completely insulating throughout the quantized Hall plateau regime