Aspects of elelctron transport in semiconductor nanostructures

Overview & Synopsis

In this thesis transport properties are studied of systems which are smaller than some characteristic coherence length. The main part of the thesis deals with quantum transport in a two-dimensional electron gas (2DEG), present at the interface of a semiconductor heterostructure. Small conductors can be defined in the 2DEG, through which an electron propagates phase-coherently. In the introductory first chapter some basic theoretical concepts of quantum transport in such systems are reviewed. Depending on the siez of the conductor various transport regimes can be probed. The emphasis will be on the quantum ballistic regime, in which transport takes place through one-dimensional subbands. The Landauer formula relates the conductance of the system to the quantum mechanical transmission coefficient of the subbands. this formula allows for a simple interpretation of the quantized conductance of a short and narrow constriction in a 2DEG. The transmission coefficient of typical systems can often be calculated in the adiabatic limit. the geometrical requirements for local adiabaticity are discussed. Global adiabaticity can be obtained in a magnetic field of sufficient strength. The magnetotransport in this regime in conveniently described using the concept of edge channels. In chapter 2 we study the magneto-transport properties of an array of 15 coupled quantum dots, defined in the 2DEG [28,29]. At a fixed magnetic field of 2 T, two types of oscillations with different amplitude and period are observed in the conductance as a function of the gate-voltage. With the help of a simple model, which makes use of the concept of adiabatically transmitted edge channels, we relate the oscillations to the formation of a mini-band structure in the system, including energy gaps and mini-bands which contain 15 discrete states. In chapter 3 we study the effect of transport- and gate-voltage fluctuations on the conductance quantization [42]. They give rise to transitions between the adiabatic transport channels. Intra-channel scattering is stronger than inter-channel scattering and transport voltage fluctuations contribute more than those of the gate-voltage. The effect of transport voltage fluctuations is characterized by a universal low-frequency behaviour. They suppress the conductance quantization found in more ideal systems. With increasing strength of the fluctuations a gap develops in the I-V characteristics of the constriction. We also calculate the frequency dependent conductance in case of a fluctuating classical potential. In chapter 4 we propose a simple device based on quantum adiabatic transport that can work as an electron pump [54]. It consists of two gates to which an alternating voltage is applied with a relative phase shift, which breaks the time reversal symmetry. Its operation relies on the Pauli principle, which leads to a distinction for the electrons transmitted through the device between inelastic emission and absorption processes. Depending on the modulation amplitude, transmission of one electron per photon or of few electrons per cycle can be realized. It is also possible to measure the electron velocity. Since inelastic processes occur in a controlled way, the device can serve to test assumptions about electron reservoirs in the presence of phase breaking. The photovoltaic effect due to gate-voltage modulations in an assymetric constriction is studied in chapter 5 [51]. Taking a simple system as an example we show that, under certain conditions, an integer amount of electrons per absorbed photon or per cycle can be transmitted. The interaction with the modulation mainly occurs in some resonant points along the constriction. In the last chapter the transport properties are discussed of a superconductor which is smaller than the temperature-dependent coherence length. We study the nonlocal correction to the normal conductivity abote T.. due to fluctuations of the superconducting order parameter; A very transparent manifestation of the nonlocal resistance corrections can be obtained in a ring geometry, where the nonlocal contributions can be detected due to their (periodic) flux dependence. We calculate the correction within the framework of the time dependent Ginzburg-Landau theory for temperatures slightly above T.., as well as far from the transition. The nonlocal character of the correction can be made visible by a four-terminal measurement, when two voltages are measured by two sets of contacts. This allows for a possible experimental test of a model