The aim of this work is to investigate some of the properties of one- and two-dimensional systems, in particular, those concerned with electrical conduction. In the quantum mechanical regime such systems have exhibited a range of interesting and potentially useful characteristics. The Landauer-Buttiker formalism has shown that the quantity which determines the resistance in mesoscopic systems is the quantum-mechanical transmission. For a strictly one-dimensional system the transmission is easily evaluated for different arrays of model potentials. Results show that the resistance increases exponentially with length as the system becomes long. For shorter systems the degree of localisation of electronic states is investigated. A time-dependent approach is adopted to calculate the transmission in the case of quasi-one-dimensional quantum wires. This requires a modification of the simple (zero temperature) Landauer conductance formula to accommodate a wave packet of finite width in momentum space. The method developed is fast, efficient and is easily adapted to study quantum wires of differing geometry, an important factor when transport is ballistic. The effect of the finite width of the wave packet is investigated. The time-dependent approach is also extended to model the Coulomb repulsion between electrons; this is applied to electron tunnelling through a quantum dot. In addition, a suitable propagation scheme for the conductance calculation allows the inclusion of a magnetic field. The effect of a transverse field on point contact conductance is considered. As a further example, the question of transport in a model lateral surface superlattice potential is addressed. Again, the finite width of the wave packet is important.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:737462 |
| Date | January 1993 |
| Creators | Stratford, Kevin |
| Publisher | University of Leicester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/2381/35801 |
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