Browsing by Author "Geisler, Martin Christoph"

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The Hofstadter butterfly and quantum interferences in modulated 2-dimensional electron systems
(2005) Geisler, Martin Christoph; Klitzing, Klaus von (Prof. Dr.)
In this work, we studied 2D electron systems in a 2D periodically modulated electric potential by means of magnetotransport measurements. Such experiments have been performed for more than a decade, using GaAs/AlGaAs heterostructures, in the search for effects caused by an artificial band structure and due to the competition of characteristic length scales in the system. Here we present samples with modulations of 100nm periodicity and with the highest reported mean free path to date, thus enabling the measurement of previously-unobserved quantum mechanical phenomena in 2D modulated electron systems. We present the fundamental concepts necessary to discuss 1D- and 2D-modulated 2D electron systems: the competition of two characteristic length scales, the modulation period and the magnetic length, leads to semiclassical commensurability oscillations in the longitudinal magnetoresistance of 1D-modulated samples. For the high magnetic field limit and a 2D modulation, this competition leads to a quantum mechanical phenomenon: the Hofstadter butterfly spectrum. We highlight its influence on magnetotransport measurements, in particular on the quantized Hall conductance. The fractal Hofstadter butterfly energy spectrum is unveiled, using the quantized Hall conductivity as a probe. The long searched-for rearrangement and deformation of this spectrum due to Landau band coupling is presented. For the weak magnetic field limit, we start with the miniband structure due to the artificial modulation and discuss Fermi contours and their modifications due to magnetic breakthrough. We describe how closed electron trajectories are manifested in magnetotransport. Quantum interferences characteristic of a 2D artificial crystal and the set of most probable electron orbits are measured and explained quantitatively for the first time. We use Fourier-transformed magnetotransport data for a range of electron densities to identify oscillations in comparison with Monte Carlo simulations which were developed in this work. Finally, we vary the lattice geometry: both a smaller lattice period and a Lieb lattice are studied in light of quantum interferences. An unexpected avoided cross over of two oscillations is found. The sensitivity of the quantum interferences to the modulation potential shape is confirmed, and new interferences are discovered. We verify a recent theoretical prediction for rectangular lattices experimentally. We observe a characteristic non-monotonic dependence of the commensurability oscillation amplitudes on the applied B-field, which is unknown for square lattices.