Microscopic details of stripes and bubbles in the quantum Hall regime

We use a fully self-consistent laterally resolved Hartree-Fock approximation for numerically addressing the electron configurations at higher Landau levels in the quantum Hall regime for nearmacroscopic sample sizes. At low disorder we find, spatially-resolved, stripe- and bubble-like charge density modulations and show how these emerge depending on the filling factor. The microscopic details of these boundary regions determine the geometrical boundary conditions for aligning the charge density modulation either as stripes or bubbles. Transport is modelled using a non-equilibrium network model giving a pronounced anisotropy in direction of the injected current in the stripe regime close to half filling. We obtain a stripe period of 2.9 cyclotron radii. Our results provide an intuitive understanding of its consequences in strong magnetic fields and indicate the dominance of many particle physics in the integer quantum Hall regime when studied at legnth scales

Linking Non-equilibrium Transport with the Many Particle Fermi Sea in the Quantum Hall Regime

The communication of the electron system with the outside world at low excitation transport experiments happens by exchanging electrons at the Fermi level. We argue that the locations where this is possible in the quantum Hall effect regime are the so-called edge channels. We explain that these channels can be understood as a more general representation of the many-particle quantum Hall (QH) system close to equilibrium that allows describing transport due to non-equilibrium on a very fundamental level. Based on fundamental principles of quantum physics, a transfer matrix formulation for the local non-equilibrium electrochemical potential in a network of interconnected directed quantum channels can be used to solve the lateral distribution of the non-equilibrium excitation potentials. Instead of using the Landauer formula or other tools like the Kubo formula for addressing conductance’s just a transfer matrix formulation for the transfer of electrochemical potentials is used to find the self-consistent lateral distribution of the non-equilibrium electrochemical potentials. Currents and potentials that are measured at contacts are only calculated as a post-processing step right at the contacts, and they allow calculating all the resistances and conductance’s like known from QH experiments. The interplay between transport and the many-particle system is of general interest when dealing with accessing information about quantum systems. Our approach allows modeling electron systems in the QH regime for realistic sample geometries, including inhomogeneities, like present in real samples or that are forced by gate electrodes as well as the random disorder potential. We combine our network model for transport with the Hartree–Fock method that allows the inclusion of realistic screening effects as well as the magnetic field-dependent enhanced g-factor

Imaging of condensed quantum states in the quantum hall effect regime

It has been proposed already some time ago that Wigner crystallization in the tails of the Landau levels may play an important role in the quantum Hall regime. Here we use numerical simulations for modelling condensed quantum states and propose real space imaging of such highly correlated electron states by scanning gate microscopy (SGM). The ingredients for our modelling are a many particle model that combines a self-consistent Hartree-Fock calculation for the steady state with a nonequilibrium network model for the electron transport. If there exist condensed many particle quantum states in our electronic model system, our simulations demonstrate that the response pattern of the total sample current as a function of the SGM tip position delivers detailed information about the geometry of the underlying quantum state. For the case of a ring shaped dot potential in the few electron limit it is possible to find regimes with a rigid (condensed) charge distribution in the ring, where the SGM pattern corresponds to the probability density of the quantum states. The existence of the SGM image can be interpreted as the manifestation of an electron solid, since the pattern generation of the charge distribution requires certain stability against the moving tip potential

A systematic study of non-ideal contacts in integer quantum Hall systems

In the present article we investigate the influence of the contact region on the distribution of the chemical potential in integer quantum Hall samples, as well as the longitudinal and Hall resistance as a function of the magnetic field. First we use a standard quantum Hall sample geometry and analyse the influence of the length of the leads where current enters/leaves the sample and the ratio of the contact width to the width of these leads. Furthermore we investigate potential barriers in the current injecting leads and the measurement arms in order to simulate non-ideal contacts. Second we simulate nonlocal quantum Hall samples with applied gating voltage at the metallic contacts. For such samples it has been found experimentally that both the longitudinal and Hall resistance as a function of the magnetic field can change significantly. Using the nonequilibrium network model we are able to reproduce most qualitative features of the experiments.Comment: 29 pages, 16 Figure

Jamming transitions in cancer

The traditional picture of tissues, where they are treated as liquids defined by properties such as surface tension or viscosity has been redefined during the last few decades by the more fundamental question: under which conditions do tissues display liquid-like or solid-like behaviour? As a result, basic concepts arising from the treatment of tissues as solid matter, such as cellular jamming and glassy tissues, have shifted into the current focus of biophysical research. Here, we review recent works examining the phase states of tissue with an emphasis on jamming transitions in cancer. When metastasis occurs, cells gain the ability to leave the primary tumour and infiltrate other parts of the body. Recent studies have shown that a linkage between an unjamming transition and tumour progression indeed exists, which could be of importance when designing surgery and treatment approaches for cancer patient