Degree Name

Doctor of Philosophy


Department of Physics


In this thesis we investigate the influence of an additional periodic modulation potential which is weak, either electric or magnetic in nature, and spatially modulated along one dimension, on the equilibrium thermodynamic and dielectric response properties of a two-dimensional electron gas in the presence of an externally applied perpendicular magnetic field.

The application of an additional modulation potential results in a broadening of the Landau level energy spectrum into bands whose widths oscillate as a function of the externally applied magnetic field. Such oscillations are found to reflect the commensurability between the two different length scales present in the system, namely the cyclotron diameter at the chemical potential and the period of the modulation. We show that such commensurability effects are also to be found in all thermodynamic quantities of the system which, in the case of a magnetic modulation, are shown for the first time. They appear at low magnetic fields as an amplitude modulation of the well-known de Haas-van Alphen-type oscillations, familiar from the homogeneous two-dimensional electron gas system in an external magnetic field which may or may not be resolved depending on temperature, and are only weakly dependent on temperature. Their origin is attributed to the oscillations occurring in the bandwidths and are consequently completely different in origin from the usual de Haas-van Alphen-type oscillations. We also find that the resulting commensurability oscillations in each thermodynamic function exhibit well-defined phase relations between the electric and magnetic modulations except in the case of the orbital magnetisation and the orbital magnetic susceptibility.

The dynamical dielectric response function and collective excitations for such weak spatially modulated systems are also calculated within the random-phase approximation. It is found that the dynamical dielectric response function is not only broadened by the additional spatial modulation, it also contains a series of subsingularities at the band edges. The origin of the new subsingularities is related to the transition energies near the van Hove singularities of the energy bands attributed to the modulation-induced broadening of the energy spectrum. This broadening, being non-uniform, leads to the reintroduction of particle-hole pair excitations into the dielectric response function. Such broadening of the response function is also found to modify the magnetoplasmon modes of such systems over their unmodulated counterpart. The broadened Landau levels allow for a new low-frequency intramagnetoplasmon mode to occur which exhibits oscillatory behaviour as a function of the external magnetic field. It is also shown that additional modulation-induced oscillations occur in the inter-magnetoplasmon spectrum, which is split into the principal and the Bernstein modes. All such oscillations reflect the ubiquitous commensurability oscillations now found in these weakly modulated systems as a function of the external magnetic field.