Linear and Nonlinear Transport in Quantum Nanostructures

Abstract: In this thesis, electron transport in mesoscopic semiconductor nanostructures, in particular so-called electron billiards or quantum dots, is studied. The thesis can be divided into two areas: the linear response regime of transport, and the nonlinear response regime of transport. The classical and quantum mechanical electron dynamics are studied for triangular and square-shaped electron billiards in the linear response regime of transport. It is shown that the temperature averaged magnetoconductance can be well understood in a semi-classical single-electron picture, in which the elecrons move on classical trajectories determined by the shape of the cavity. Studied in the phase coherent regime as a function of magnetic field or Fermi energy, the conductance fluctuations, which are due to wave interference, can also be related to certain classical orbits. In the nonlinear regime of transport, it is found that the conductance of asymmetric quantum dots is asymmetric with respect to zero bias. This leads to an average net current, when an AC voltage is applied over the device, and the devices are often referred to as quantum ratchets. In the phase coherent regime, the asymmetry of the conductance is clearly related to the effect of an electric field on the electron states inside the dot. The observed asymmetry is sensitively dependent on the amplitude of the applied bias, on the magnetic field, and on the Fermi energy. The importance of the designed dot geometry is significant, as compared to unintentional imperfections, such as impurities and fabrication inaccuracies. In the tunneling regime, the net current direction can be predicted from the shape of the tunneling barrier, and the direction can be changed by simply changing the temperature. Rectification is also studied in artificial materials, consisting of nanometer-sized asymmetric scatterers, arranged in a two-dimensional lattice. At room temperature, the output is determined by ballistic scattering and electric field collimation, whereas at liquid helium temperatures, the output is believed to be dominated by the changed angular distribution, due to mode opening, and collimation caused by the applied voltage.