Open Collections

The existence of singular terms and their effects on the validity of Fermi liquid theory in two dimensions

University of British Columbia

The question of the breakdown of Fermi liquid theory in two dimensions is examined in the context of perturbation theory for a dilute interacting Fermi gas. The quasiparticle interaction function, fic;u;, is calculated for such a system. The interaction function, calculated to second order in terms of the dimensionless coupling constant, shows various singularities. The most divergent terms appear in the cross channel, but cancel out leaving a much weaker singularity in the limit of two moment a approaching each other (0 —f 0 ). As in the case of the three dimensional Fermi gas, the Cooper channel contains a logarithmic singularity in the limit 0 —f 7r. This singularity can be summed and is known to be harmless to the structure of Fermi liquid theory. A different feature in two dimensions is the existence of such a singularity for 0 —p 0. This feature needs further investigation. Calculations have also been extended to a polarized Fermi gas and the result is equivalent to the unpolarized case and does not show any additional features. In conclusion, the results do not indicate the presence of strong divergences which could cause the breakdown of Fermi liquid theory in two dimensions for a dilute interacting Fermi gas.

Thesis/Dissertation

application/pdf

2008-09-15

For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

http://hdl.handle.net/2429/1995

Physics

University of British Columbia

UBCV

DSpace