Screening model of metallic nonideal contacts in the integer quantized Hall regime

Abstract

In this work, we calculate the electron and the current density distributions both at the edges and the bulk of a two dimensional electron system, focusing on ideal and non-ideal contacts. A three dimensional Poisson equation is solved self-consistently to obtain the potential profile in the absence of an external magnetic field considering a Hall bar defined both by gates (contacts) and etching (lateral confinement). In the presence of a perpendicular magnetic field, we obtain the spatial distribution of the incompressible strips, taking into account the electron-electron interactions within the Thomas-Fermi approximation. Using a local version of Ohms law, together with a relevant conductivity model, we also calculate the current distribution. We observe that the incompressible strips can reside either on the edge or at the bulk depending on the field strength. Our numerical results show that, due to a density poor region just in front of the contacts, the incompressible strips do not penetrate to the injection region when considering non-ideal contact configuration. Such a non-ideal contact is in strong contrast with the conventional edge channel pictures, hence has a strong influence on transport. We also take into account heating effects in a phenomenological manner and propose a current injection mechanism from the compressible regions to the incompressible regions. The model presented here perfectly agrees with the local probe experiments all together with the formation of hot-spots.

Time-dependent transport in Aharonov–Bohm interferometers

“…This case is called the 'leaky' incompressible state, which can be accurately determined by taking into account the collision broadened Landau level width and the extent of the wave function. Once the strip becomes even smaller than the wave extent, the classical Hall effect is observed [22], as shown in figure 1(d). Altogether, interference can be observed at the lower end of the quantized Hall plateau.…”

“…In each iteration step a relative accuracy threshold of <10 −6 is obtained for the density. This standard calculation scheme has previously been used to describe similar systems successfully [16,[21][22][23].…”

The visibility of IQHE at sharp edges: experimental proposals based on interactions and edge electrostatics

“…Nevertheless, for numerical calculations one starts with T = 0, B = 0 profiles, increases the temperature, then adds the quantizing magnetic field via DOS and decreases the temperature step by step till the numerical accuracy is obtained. Further details of the self-consistent calculation scheme can be found in the literature, which is applied successfully to systems that assume translational invariance in the y-direction, considering single layers [9,15,28,38,39], double layers [40][41][42] and actual 2D systems [12,26,43]. This approach is known as the screening theory and its predictions are confirmed experimentally [24,25,[44][45][46][47][48].…”

“…The corresponding incompressible strip and current distributions are shown in figures 3(b)-(e). The results of rigorous self-consistent calculations have been published elsewhere [26,49]; however, below we will provide a brief discussion that describes how to obtain current distribution from local filling factors.…”

“…The theoretical investigations, known as the screening theory, aim to clarify the effects of the boundary electrostatics [7,[10][11][12], temperature [13,14] and current [15,16] on the formation of incompressible strips. More recently, the behavior of the incompressible strips near the contacts was investigated experimentally [22] and theoretically [26]. These investigations helped to resolve the long-standing question of what characteristics define an ideal contact.…”