Consequences of a possible adiabatic transition between nu=1/3 and nu=1 quantum Hall states in a narrow wire

We consider the possibility of creating an adiabatic transition through a narrow neck, or point contact, between two different quantized Hall states that have the same number of edge modes, such as nu = 1 and nu = 1/3. We apply both the composite-fermion and Luttinger-liquid formalism to analyze the transition. We suggest that using such adiabatic junctions one could build a de step-up transformer, where the output voltage is higher than the input. Difficulties standing in the way of an experimental implementation of the adiabatic junction are addressed. [S0163-1829(98)02104-3]

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

Many-Body Effects on Tunneling of Electrons in Magnetic-Field-Induced Quasi One-Dimensional Electron Systems in Semiconductor Nanowhiskers

Effects of the electron-electron interaction on tunneling in a semiconductor nanowhisker are studied in a magnetic quantum limit. We consider the system with which bulk and edge states coexist. In bulk states, the temperature dependence of the transmission probability is qualitatively similar to that of a one-dimensional electron system. We investigate contributions of edge states on transmission probability in bulk states. Those contributions can be neglected within our approximation which takes into account only most divergent terms at low temperatures.Comment: 9 pages, 6 figure

Electron Depletion Due to Bias of a T-Shaped Field-Effect Transistor

A T-shaped field-effect transistor, made out of a pair of two-dimensional electron gases, is modeled and studied. A simple numerical model is developed to study the electron distribution vs. applied gate voltage for different gate lengths. The model is then improved to account for depletion and the width of the two-dimensional electron gases. The results are then compared to the experimental ones and to some approximate analytical calculations and are found to be in good agreement with them.Comment: 16 pages, LaTex (RevTex), 8 fig

Experimental investigation of the edge states structure at fractional filling factors

We experimentally study electron transport between edge states in the fractional quantum Hall effect regime. We find an anomalous increase of the transport across the 2/3 incompressible fractional stripe in comparison with theoretical predictions for the smooth edge potential profile. We interpret our results as a first experimental demonstration of the intrinsic structure of the incompressible stripes arising at the sample edge in the fractional quantum Hall effect regime.Comment: 5 pages, 5 figures included. Submitted to JETP Letter

Charge and current oscillations in Fractional quantum Hall systems with edges

Stationary solutions of the Chern-Simons effective field theory for the fractional quantum Hall systems with edges are presented for Hall bar, disk and annulus. In the infinitely long Hall bar geometry (non compact case), the charge density is shown to be monotonic inside the sample. In sharp contrast, spatial oscillatory modes of charge density are found for the two circular geometries, which indicate that in systems with compact geometry, charge and current exist also far from the edges.Comment: 16 pages, 6 figures Revte

A Complex Network Approach to Topographical Connections

The neuronal networks in the mammals cortex are characterized by the coexistence of hierarchy, modularity, short and long range interactions, spatial correlations, and topographical connections. Particularly interesting, the latter type of organization implies special demands on the evolutionary and ontogenetic systems in order to achieve precise maps preserving spatial adjacencies, even at the expense of isometry. Although object of intensive biological research, the elucidation of the main anatomic-functional purposes of the ubiquitous topographical connections in the mammals brain remains an elusive issue. The present work reports on how recent results from complex network formalism can be used to quantify and model the effect of topographical connections between neuronal cells over a number of relevant network properties such as connectivity, adjacency, and information broadcasting. While the topographical mapping between two cortical modules are achieved by connecting nearest cells from each module, three kinds of network models are adopted for implementing intracortical connections (ICC), including random, preferential-attachment, and short-range networks. It is shown that, though spatially uniform and simple, topographical connections between modules can lead to major changes in the network properties, fostering more effective intercommunication between the involved neuronal cells and modules. The possible implications of such effects on cortical operation are discussed.Comment: 5 pages, 5 figure

The Structure of Fractional Edge States: A Composite Fermion Approach

I study the structure of the two-dimensional electron gas edge in the quantum Hall regime using the composite fermion approach. The electron density distribution and the composite fermion energy spectrum are obtained numerically in Hartree approximation for bulk filling factors $\nu=1,1/3,2/3,1/5$. For a very sharp edge of the $\nu=1$ state the one-electron picture is valid. As the edge width $a$ is increased the density distribution shows features related to the fractional states and new fractional channels appear in pairs. For a very smooth edge I find quasiclassically the number of channels $p\sim\sqrt{a/l_H}$, where $l_H$ is the magnetic length.Comment: 10 pages, RevTex, 6 uuencoded figures appende

Conductance fluctuations at the integer quantum Hall plateau transition

We study numerically conductance fluctuations near the integer quantum Hall effect plateau transition. The system is presumed to be in a mesoscopic regime, with phase coherence length comparable to the system size. We focus on a two-terminal conductance G for square samples, considering both periodic and open boundary conditions transverse to the current. At the plateau transition, G is broadly distributed, with a distribution function close to uniform on the interval between zero and one in units of e^2/h. Our results are consistent with a recent experiment by Cobden and Kogan on a mesoscopic quantum Hall effect sample.Comment: minor changes, 5 pages LaTex, 7 postscript figures included using epsf; to be published Phys. Rev. B 55 (1997

Collapse of Spin-Splitting in the Quantum Hall Effect

It is known experimentally that at not very large filling factors $\nu$ the quantum Hall conductivity peaks corresponding to the same Landau level number $N$ and two different spin orientations are well separated. These peaks occur at half-integer filling factors $\nu = 2 N + 1/2$ and $\nu = 2 N + 3/2$ so that the distance between them $\delta\nu$ is unity. As $\nu$ increases $\delta\nu$ shrinks. Near certain $N = N_c$ two peaks abruptly merge into a single peak at $\nu = 2N + 1$. We argue that this collapse of the spin-splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron $g$-factor. We use the mean-field approach to show that in the limit of zero Zeeman energy $\delta\nu$ experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for $N_c$ in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures $N_c = 0.9 d n^{5/6} n_i^{-1/3},$ where $d$ is the spacer width, $n$ is the density of the two-dimensional electron gas, and $n_i$ is the two-dimensional density of randomly situated remote donors.Comment: 14 pages, compressed Postscript fil