We present line-and area-scans of the Hall potential landscape of a twodimensional electron system (2DES) in narrow (AlGa)As-based Hall bars under quantum Hall (QH) conditions, obtained by low-temperature scanning force microscopy. For several magnetic field values B in the regime of the QH plateau with Landau level filling factor ν = 2, we measured the evolution of the Hall potential profiles and of the longitudinal voltage drop along the Hall bar as a function of increasing voltage/current bias, leading finally to the electrically induced breakdown of the quantum Hall effect (QHE). Basically two types of evolution were observed: for the low B-field side of the QHE plateau, two distinct Hall potential drops appear close to the two edges of a cross section, equally distributed at low bias but continuously developing to an asymmetrical distribution with increasing bias. At high bias, a steady increase of the longitudinal voltage drop is observed, accompanied by a rising slope of the Hall potential drop in the bulk. For the upper B-field side of the QH plateau, the Hall voltage drops are broadly distributed across the whole cross section, and the distribution remains almost unchanged until the bias reaches a critical value where the Hall potential profile changes rather abruptly, enhancing locally the Hall field. Beyond this, with further increase of the bias, a steep rise of the longitudinal voltage drop is detected. These findings are naturally explained in the microscopic picture of the QHE, based on the self-consistent evolution of the Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. compressible and incompressible landscape inside the 2DES with increasing bias.Keywords: quantum Hall effect, breakdown of the QHE, incompressible stripes, scanning force microscopy, current distribution, Hall potential landscape 1 Layer sequence for sample A: on top of a semi-insulating GaAs substrate, a GaAs/AlGaAs superlattice 50x (10 nm, 10 nm) was grown, followed by 500 nm GaAs, 20 nm AlGaAs spacer, 25 nm AlGaAs doped with Si, 5 nm AlGaAs, and, finally, 5 nm GaAs as cap layer. For sample B, the AlGaAs spacer layer was 25 nm thick, the AlGaAs:Si doping layer 20 nm. 2 New J. Phys. 16 (2014) 113071 K Panos et al

First, we present recent experimental results confirming previously predicted strong asymmetries of the current distribution in narrow Hall bars under conditions of the integer quantum Hall effect (IQHE). Then, using a previously developed self-consistent screening and transport theory of the IQHE, we investigate how these asymmetries, which are due to a nonlinear feedback effect of the imposed current on the electron distribution in the sample, depend on relevant parameters, such as strength of the imposed current, magnetic field, temperature and collision broadening of the Landau-quantized energy bands. We find that many aspects of the experimental results can be understood within this approach, whereas other aspects require explicit consideration of additional mechanisms, which may lead to the breakdown of the IQHE. Contents

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Classical microscopic nonrelativistic calculations are made for collisions between equal mass nuclei projectile and target with A = A = 20 for laboratory energies E = 117, 400 and 800 MeV/A and also between nuclei with Ap = A T = 40 for E = 400 MeV/A^. For a given initial configuration of the projectile and target nucléons the trajectories of all nucléons are calculated classically with two-body forces between all pairs of nucléons.The implementation of the CEOM calculations is presented and discussed in detail, in particular its four aspects, namely: the choice of the 2-body potentials, choice of initial configurations, the Α-body trajectory calcula tions, and the analysis of these.Nonrelativistic calculations are made for two types of potentials. A static potential, which consists of a sum of reasonable attractive and repul sive Yukawa potentials and which is adjusted to give reasonable binding energies and also to fit the average sin 2 8 weighted nucleon-nucleon cross section, which emphasizes transverse momentum transfers. The other type of potential is a scattering equivalent momentum dependent potential which is generated from the original static potential by a suitable canonical trans formation and which gives the identical asymptotic two-body trajectories as the static potential. More limited relativistic calculations for single initial configurations are also made. These are relativistic to order V 2 /c 2 and use a retarded potential.The configurations representing the initial nuclei are chosen to have a reasonable radius and kinetic energy; however, they do not saturate with 146 4.3 NONCENTRAL COLLISIONS 180

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