Browsing by Subject "Quantum hall effect"
Now showing 1 - 6 of 6
Results Per Page
Sort Options
Item Open Access Analytic calculation of ground state properties of the 2d and 3d electron gas(2015-06) Katı, YağmurThe electron gas (2D and 3D) is a model which consists of interacting electrons moving in a uniform positive background. Its importance stems from the fact that a number of metals behave similarly, it provides the functional used in density functional theory, and that in 2D it can be experimentally realized. Understanding the behavior of this model is of fundamental importance. In this thesis we present an analysis of this model based on the Hypernetted Chain Method in 3D, and 2D. The HNC method is a variational method to calculate the ground state properties of an interacting system, by expressing the ground state energy as a functional of the radial distribution function. Minimizing the energy expression one obtains a zero energy Schr odinger equation for the square root of the radial distribution function. The potential in this equation can include the e ects of fermionic or bosonic exchange. We applied this method to charged boson and electron gas in 2D and 3D systems. On the basis of the results of this research, it can be concluded that we obtained very close correlation energy results compared to Monte Carlo, and FHNC results for the density range when rs is from 0 to 20. This extended range is important for solid state applications.Item Open Access Complementary and alternative technique for the determination of electron effective mass: Quantum hall effect(Taylor & Francis Inc., 2016) Ardalı, S.; Tiras, E.; Arslan, E.; Özbay, EkmelThe quantum Hall effect measurements in the AlInN/AlN/GaN heterostructure are studied in the temperature range from 1.8 K to 14 K and a magnetic field up to 11 T. The quantized two-dimensional electron gas was placed at the AlN/GaN interface. The Hall resistance of two-dimensional electron gas has been found to be quantized at multiple integers of von Klitzing constant that refers to the integer quantum Hall effect. The experimental data have been used to determine the Fermi energy, carrier density, and effective mass two-dimensional electrons. The results are in agreement with those derived from the longitudinal magnetoresistance in the same structure.Item Open Access Landau levels in lattices with long - range hopping(American Physical Society, 2013) Atakişi, Hakan; Oktel, M. ÖzgürLandau levels (LLs) are broadened in the presence of a periodic potential, forming a barrier for accurate simulation of the fractional quantum Hall effect using cold atoms in optical lattices. Recently, it has been shown that the degeneracy of the lowest Landau level (LLL) can be restored in a tight-binding lattice if a particular form of long-range hopping is introduced. In this paper, we investigate three problems related to such quantum Hall parent Hamiltonians in lattices. First, we show that there are infinitely many long-range hopping models in which a massively degenerate manifold is formed by lattice discretizations of wave functions in the continuum LLL. We then give a general method to construct such models, which is applicable to not only the LLL but also higher LLs. We use this method to give an analytic expression for the hoppings that restores the LLL, and an integral expression for the next LL. We also consider whether the space spanned by discretized LL wave functions is as large as the space spanned by continuum wave functions, and we find the constraints on the magnetic field for this condition to be satisfied. Finally, using these constraints and the first Chern numbers, we identify the bands of the Hofstadter butterfly that correspond to continuum LLs.Item Open Access Local current distribution at large quantum dots (QDs): A self-consistent screening model(Elsevier B.V., 2008) Krishna, P. M.; Siddiki, A.; Güven, K.; Hakioǧlu T.We report the implementation of the self-consistent Thomas-Fermi screening theory, together with the local Ohm's law to a quantum dot system in order to obtain local current distribution within the dot and at the leads. We consider a large dot (size > 700 nm) defined by split gates, and coupled to the leads. Numerical calculations show that the non-dissipative current is confined to the incompressible strips. Due to the non-linear screening properties of the 2DES at low temperatures, this distribution is highly sensitive to external magnetic field. Our findings support the phenomenological models provided by the experimental studies so far, where the formation of the (direct) edge channels dominate the transport.Item Open Access The self-consistent calculation of the edge states at quantum Hall effect (QHE) based Mach-Zehnder interferometers (MZI)(Elsevier B.V., 2008) Siddiki, A.; Kavruk, A. E.; Öztürk, T.; Atav, U.; Şahin, M.; Hakioǧlu T.The spatial distribution of the incompressible edge states (IES) is obtained for a geometry which is topologically equivalent to an electronic Mach-Zehnder interferometer, taking into account the electron-electron interactions within a Hartree type self-consistent model. The magnetic field dependence of these IES is investigated and it is found that an interference pattern may be observed if two IES merge or come very close, near the quantum point contacts. Our calculations demonstrate that, being in a quantized Hall plateau does not guarantee observing the interference behavior.Item Open Access A self-consistent microscopic model of Coulomb interaction in a bilayer system as an origin of Drag Effect Phenomenon(Elsevier B.V., 2008) Güven, K.; Siddiki, A.; Krishna, P. M.; Hakioǧlu T.In this work we implement the self-consistent Thomas-Fermi model that also incorporates a local conductivity model to an electron-electron bilayer system, in order to describe novel magneto-transport properties such as the Drag Phenomenon. The model can successfully account for the poor screening of the potential within the incompressible strips and its impact on the inter-layer Coulomb interaction. An externally applied current in the active layer results in the tilting of the Landau levels and built-up of a Hall potential across the layer, which, in turn, induces a tilted potential profile in the passive layer as well. We investigate the effect of the current intensity, temperature, magnetic field, and unequal density of layers on the self-consistent density and potential profiles of the bilayer system.