Anisotropic Fermionic Quasiparticles

We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction, in the presence of bare mass anisotropy (i.e. with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading order dynamical self-energy approximation. We find novel anisotropic features of quasiparticle properties that are not captured by the isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are: (1) the renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the inelastic scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective mass anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system although the use of an equivalent isotropic approximation using the density-of-states effective mass works as a reasonable approximation in many situations. We also provide a theory using the plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi surface topology, finding that the elliptic shape of the bare Fermi surface is preserved, with suppressed ellipticity, in the interacting system to a high degree of accuracy. Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.