Dissertation summary

Two dimensional electron systems
in atomically precise periodic potentials

Ph. D. Dissertation of Rainer A. Deutschmann
Walter Schottky Institute
University of Technology Munich
July 27, 2001

Selected Topics of Semiconductor Physics and Technology
ISBN Number: 3-932749-42-1

In this work we introduce the superlattice field-effect transistor (SLFET), a new three-terminal semiconductor device that combines a two-dimensional electron system with a superlattice, and thus allows us to explore hitherto undisclosed low-dimensional regimes. The SLFET is fabricated with atomic precision in two spatial dimensions by molecular beam epitaxy (MBE) in the GaAs/AlGaAs lattice matched material system using the cleaved-edge overgrowth technique. In a first MBE growth step along the (001) direction, an undoped superlattice is sandwiched between the source and drain contacts. After in situ cleaving the sample, a GaAs set-back layer and a gate barrier and contact is grown in (110) direction. We have perfect control over all relevant layer thicknesses and compositions, thus by band-structure engineering we can design any system between an array of weakly coupled quantum wires, to a two-dimensional electron system with wide minibands and narrow minigaps. We investigate these systems in low temperature electronic transport experiments, either by equilibrium magnetotransport, or non-equilibrium current-voltage measurements. Theoretical models are developed using semi-classical and quantum mechanical methods.

The artificial band structures, obtained with the SLFETs, represent energy scales (e.g. miniband width or subband spacing), that are of comparable magnitude to other experimentally controllable energy scales, such as the Fermi energy, the magnetic and potential energy, and temperature. This sets us in a position to explore band structure effects in a variety of systems over a wide parameter space. We have sectioned this work according to the miniband width of
the SLFET under study.

Magnetotransport in the lowest miniband of width 3.3 meV reveals a cross-over from a two-dimensional behavior, characterized by closed electron orbits and magnetoresistance oscillations, to a one-dimensional behavior, manifested by open electron orbits and quenching of magneto-quantum oscillations, as the Fermi energy is raised from within the miniband into the band gap. For large magnetic fields, closed electron orbits are recovered due to magnetic breakdown. For the first time we directly confirm the theoretically expected breakdown field. We can explain all experimental data within a semiclassical model, and gain additional insight with a new quantum mechanical description by directly calculating the density of states in a non-perturbative way.

For a series of SLFETs with miniband widths between 3.3 meV and 21.2 meV, in high field miniband transport experiments we discover negative differential resistance in qualitative agreement with the Esaki-Tsu model. Additional current maxima are explained by resonant emission of folded acoustic phonons through Bloch-oscillating electrons. The two-dimensionality of the electron system together with the presence of a metallic gate serve to stabilize the charge density in the negative differential velocity regime.

In weakly coupled quantum wires we observe transport in the resonant tunneling regime involving the wire ground and first excited states. Magnetic fields applied perpendicular to the wires, either parallel or perpendicular to the current direction, change the position of the resonance peaks as well as the tunneling current. Our model is based on the simultaneous conservation of electron energy and momentum in the tunneling process, the magnetically induced spatial separation of forward and reverse moving electrons within each wire and the distortion of the tunneling path in a magnetic field, and the formation of wire Landau levels at high magnetic fields.

In weakly modulated two-dimensional electron systems, for the first time we directly visualize the text-book case of a one-dimensional band structure. Our observation is explained semiclassically as quantum interference in artificial band structures. The first type of quantum interference effect occurs in closed electron orbits, in part made possible by magnetic breakdown of the small energy gaps separating formerly unconnected electron trajectories. The second type of quantum interference effect relates two different open electron orbits and results in a magnetic field dependent back-scattering probability. This process corresponds to the Aharonov-Bohm effect in reciprocal space. The known Weiss (commensurability) oscillations appear as a special case of our theory, and are thus, for the first time, explained by the topology of the artificial band structure.

Owing to the unparalleled combination of high electron mobility and density tunability in very weakly modulated SLFETs, we are able to discover hitherto undisclosed aspects of a ferromagnetic phase transition at fractional filling. As there exist two degenerate v=2/3 fractional quantum Hall states with different spin orientations at low electron densities, hysteresis in magnetoresistance, a non-monotonic time dependence reminiscent of the Barkhausen effect, and peculiar features in resistively detected nuclear magnetic resonance experiments are ascribed to a ferromagnetic ordering and domain morphology. Even though our results generally apply to two-dimensional electron systems, we have evidence that the potential modulation in the SLFET intensifies domain formation.

Download Ph.D. Dissertation in .pdf format (9.5 MB) diss_deutschmann2001.pdf