| In this work, we analyzed the anomalous behavior of a two dimensional interacting Fermi system. The first anomaly that has been investigated is related to the low-energy property of Fermi liquids in two dimensions. The forward scattering processes, in the second order, lead to a log divergence in the imaginary part of the self-energy on the mass shell. We found that this divergence becomes even more singular at higher orders and takes the form of a power-law, potentially leading to the breakdown of Fermi-liquid theory. We deal with the divergence by re-summing the maximally divergent terms at each order of interaction, with the result that the renormalized imaginary part of self-energy is well defined on the mass shell. We also investigated in detail the contribution of the collective modes: zero-sound mode (for a contact potential) and the plasmon mode (for a Coulomb potential) to the nonanalytic temperature (T2) dependent term in the specific heat. We found that the zero-sound mode does not make any contribution to the nonanalytic T2-dependent term in the specific heat, whereas the plasmons do make a nonanalytic contribution.;The second anomaly is the lack of experimental observation of a polarization-dependent effective mass as a function of the applied parallel magnetic field in a Si-MOSFET sample. We investigated this experimental observation in the framework of an N-component model, where N is an additional degree of freedom (which in our case is the valley degree of freedom). This model gives the change in the effective mass between an unpolarized and a fully polarized state to be not more than 1 to 3%, a result consistent with the experiment. |
