Abstract
In this thesis we present a study of quantum transport in mesoscopic structures in the low-temperature regime; the structures are small enough that the transport is coherent. A theory based on Green’s functions is constructed, including an explicit and practical approach to including the effect of a magnetic field. A single, numerically robust computational framework implementing this theory allows the calculation of not only the transmission and reflection coefficients - and therefore the electrical conductance - but also the thermoelectric coefficients and local density of states, all on a per-mode basis. Additionally, realistic models of spatially-distributed disorder can be applied to any structure and the resulting effects examined. For the purposes of comparison, this theory is applied to simple narrow wires and quantum point contacts, before using it to model much more complex single, double and U-bend structures and rectangular rings. The U-bend exhibits peaks in the transmission coefficient as a function of energy, which leads to large fluctuations in the thermopower. The ring displays the classic feature of Aharonov-Bohm-type oscillations in the transport properties as a function of magnetic field strength, as well as magnetically-enhanced resonant transmission; in the absence of a magnetic field it can also perform efficiently in terms of thermoelectric conversion, which may be of practical importance. The effect of disorder due to site-specific impurities and edge roughness is investigated, highlighting a number of interesting physical effects which are seldom discussed in the literature. Calculations of the transport properties of a U-bend in the presence of disorder show that these are quite robust. Similar calculations for the rectangular ring also show that the Aharonov-Bohm-type behaviour persists in the presence of moderate disorder - albeit somewhat chaotically - but breaks down in more disordered structures.