Akademik Veri Yönetim Sistemi
The 19th International Conference on Electronic Properties of Two-Dimensional Systems, Florida, Amerika Birleşik Devletleri, 25 - 29 Temmuz 2011, ss.1
.In three dimensions, there are two kind of particles: Fermions and Bosons, which obey Fermi-Dirac and Bose-Einstein statistics respectively. However, in two dimensions new kind of particles appear, namely anyons, which are described by fractional statistics [1, 2]. In the case of a two dimensional electron gas subject to a strong perpendicular magnetic field, these anyonic particles are called Laughlin quasi-particles and obey fractional statistics assuming fractional electric charge [3]. The quantum Hall based interferometers, has revealed a novel technique to exploit the properties of the quasi-particles, which utilizes the so called ‘edge states’ (ES) in the extreme quantum limit. The ESs are considered as monochromatic beams that carry quasi-particles without scattering. Therefore, the overall interference pattern strongly depends on the spatial distribution of these states [4, 5]. A key element of these experiments are the quantum point contacts (QPCs) and the electrostatic potential (ESP) profile near these QPCs together with the quantum dot. Electrostatics play an important role in the rearrangement of these ES [6]. In addition, the interaction of the electrons or quasi-particles was proposed to be a possible origin of the dephasing and a better understanding requires a self-consistent (SC) calculation of the ESP. Here we present an implementation of the SC-Thomas-Fermi-Poisson approach to a homogeneous two dimensional electron system [7, 8], where interferometer is defined by a quantum dot, to obtain the ESP and electron distribution at the mentioned interferometers.
In this work the widths of the incompressible strips, i.e. the edge-states, are investigated at filling factors n = 1, 2, and 1/3 in the presence of strong, perpendicular magnetic field. To find the spatial distribution of the incompressible strips, different Lande g* factors are taken into consideration, since exchange and correlations enhance it’s bulk value. We present a microscopic picture of the fractional quantum Hall effect, based on a phenomenological model. The partially occupied lowest Landau level is assumed to form an energy gap due to strong correlations, hence becomes incompressible. We adopt the findings of Jain [9] in our calculation scheme by simply including this gap to our energy spectrum and obtain the incompressible strips of n = 1/3. Such a treathment is motivated by very recent semi-classical calculations [10]. The interference conditions are investigated as a function of the gate voltage and steepness of the confinement potential, together with the strength of the applied magnetic field. We also calculate the area between the edge states which are enclosed..