A. Siddiki

The spin–split incompressible edge states within empirical Hartree approximation at intermediately large Hall samples

Abstract A self-consistent Thomas–Fermi–Poisson based calculation scheme is used to achieve spin resolved incompressible strips (ISs). The effect of exchange and correlation is incorporated by an empirically induced g factor. A local version of Ohms law describes the imposed fixed current, where the discrepancies of this model are resolved by a relevant spatial averaging process. The longitudinal resistance is obtained as a function of the perpendicular (strong) magnetic field at filling factor one and two plateaus. Interrelation between the ISs and the longitudinal zeros is explicitly shown.

The self-consistent calculation of exchange enhanced odd integer quantized Hall plateaus within Thomas–Fermi–Dirac approximation

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.

Evanescent incompressible strips as origin of the observed Hall resistance overshoot

In this work we provide a systematic explanation to the unusual non-monotonic behavior of the Hall resistance observed in two-dimensional electron systems. We use a semi-analytical model based on the interaction theory of the integer quantized Hall effect to investigate the existence of the anomalous, i.e. overshoot, Hall resistance RH. The observation of the overshoot resistance at low magnetic-field edge of the plateaus is elucidated by means of overlapping evanescent incompressible strips, formed due to strong magnetic fields and interactions. Utilizing a self-consistent numerical scheme we also show that, if the magnetic field is decreased the RH decreases to its expected value. The effects of the sample width, temperature, disorder strength and magnetic field on the overshoot peaks are investigated in detail. Based on our findings, we predict a controllable procedure to manipulate the maxima of the peaks, which can be tested experimentally. Our model does not depend on specific and intrinsic properties of the material, provided that a single-particle gap exists.

Edge electrostatics revisited

Abstract In this work we investigate in detail, the different regimes of the pioneering work of Chklovskii et al. [1] , which provides an analytical description to model the electrostatics at the edges of a two-dimensional electron gas. We take into account full electrostatics and calculate the charge distribution by solving the 3D Poisson equation self-consistently. The Chklovskii formalism is reintroduced and is employed to determine the widths of the incompressible edge-states also considering the spin degree of freedom. It is shown that, the odd integer filling fractions cannot exist for large magnetic field intervals if many-body effects are neglected. We explicitly show that, the incompressible strips which are narrower than the quantum mechanical length scales vanish. We numerically and analytically show that, the non-self-consistent picture becomes inadequate considering realistic Hall bar geometries, predicting large incompressible strips. The details of this picture are investigated considering device properties together with the many-body and the disorder effects. Moreover, we provide semi-empirical formulas to estimate realistic density distributions for different physical boundary conditions.

Theoretical investigation of local electron temperature in quantum Hall systems

Abstract In this work we solve thermo-hydrodynamical equations considering a two dimensional electron system in the integer quantum Hall regime, to calculate the spatial distribution of the local electron temperature. We start from the self-consistently calculated electrostatic and electrochemical potentials in equilibrium. Next, by imposing an external current, we investigate the variations of the electron temperature in the linear-response regime. Here a local relation between the electron density and conductivity tensor elements is assumed. Following the Ohms law we obtain local current densities and by implementing the results of the thermo-hydrodynamical theory, calculate the local electron temperature. We observe that the local electron temperature strongly depends on the formation of compressible and incompressible strips.