Far infrared magneto-optical studies of spin effects and off diagonal conductivity in the integer quantum hall regime
Stier, Andreas Volker
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The motivation for this dissertation is the study of the integer quantum Hall effect. Two different topics are explored based on the complementary theoretical view of this effect. On the one hand, topologically protected edge states contribute to the current distribution in samples containing a two dimensional electron gas in a high magnetic field. These edge channels are robust against scattering and can be viewed as one- dimensional conductors along the edges of the sample where dissipationless transport occurs. We have studied the effect of spin-orbit interaction on those edge channels. These experiments are important both from a technological point of view as well as from a fundamental scientific perspective. The former is motivated by the emerging field of spintronics and quantum computation. Within that framework, the utilization of the electrons spin is regarded as a superior method to process information and to conduct computations. The latter point is that to our knowledge the effect of spin- orbit interaction on the width and formation of edge channels has so far only theoretically been addressed. We have utilized a sensitive photoconductivity approach to study electric-dipole induced spin resonances (EDSR) between spin-split incompressible quantum Hall edge channels. Linearly polarized monochromatic far infrared radiation from a molecular gas laser induced changes in the longitudinal resistance of a two dimensional electron gas (2DEG) in an asymmetric InAs quantum well in the quantum Hall regime; the photo response (PR). We observe non resonant bolometric PR from the heating of the 2DEG, resonant bolometric PR from cyclotron resonant absorption and sharp pairs of resonance features in the vicinity of the odd filling factor v = 7 which we associate with EDSR transitions between pairs of incompressible quantum Hall edge channels. We study the behavior of the resonances as a function of angle between the sample normal and magnetic field and find an unexpected splitting of the resonance features with angle; the resonance feature which we associate with the EDSR transition from the topmost Landau level abruptly disappears below a critical angle. A study of the resonances with changed applied current reveals another unexpected behavior as that the central resonance feature splits in applied magnetic field with increased applied current. We introduce a detailed model based on the vector addition of applied and effective spin- orbit magnetic field that yields a total magnetic field which couples to the spin of the electrons in the incompressible quantum Hall edge channels. This model qualitatively reproduces all the experimentally observed effects and semi-quantitatively reproduces the splitting of two pairs of resonance features with angle. We discuss the splitting of the central resonance pair with increased current and find a mechanism explaining the possibility of the observed effect. The second part of this dissertation is based on the quantum Hall picture of localization. The electronic wavefunction in a two dimensional electron gas are bound to scattering centers, which leads to a theoretical description of the Landau level density of states that is comprised of localized and delocalized states. States are localized and therefore do not contribute to longitudinal current flow when the extent of the wavefunction is smaller than the sample size. Within a recent theory of dynamical scaling, the effective sample size is reduced in the ac regime with increasing frequency. At high frequency, the quantum Hall plateau is predicted to vanish due to the delocalization of all electronic states. We have studied a 2DEG in a GaAs/AlGaAs heterostructure close to cyclotron resonance utilizing a polarization modulation method. We measure the Faraday rotation close to cyclotron resonance as a function of frequency, temperature and 2DEG density and find for the first time features in the Faraday rotation associated with the dc integer quantum Hall effect. We analyze the features with a scaling theory and find scaling behavior favoring long range electron-electron interactions as the dominant mechanism for localization.