Journal of Experimental and Theoretical Physics Letters

Sign of the harmonics of the effective interaction in a Fermi gas with repulsion

M. A. Baranov, M. Yu. Kagan

Published Apr 1, 1996• 0 citations

Abstract

A general model-independent justification is given for the assertion that a superconducting transition is possible in a Fermi gas with repulsion. It is shown for a wide class of systems that at least one harmonic of the effective interaction is attractive. A relation is found between the harmonics of the effective interaction and the harmonics of the quasiparticle scattering amplitude in the gas approximation.

DOI: 10.1134/1.567086

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Journal of Experimental and Theoretical Physics Letters

Sign of the harmonics of the effective interaction in a Fermi gas with repulsion

M. A. Baranov, M. Yu. Kagan

Published Apr 1, 1996• 0 citations

Publisher

Abstract

DOI: 10.1134/1.567086

Related papers

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Journal de Physique IFeb 1, 199316 citations

{r}_{s}=1

{r}_{s}=37

. The density and spin-density mean fields are fitted to the compressibility and spin susceptibility of Green's-function Monte Carlo calculations and the local-field factors

G(q)

of microscopic models. We find

p

-wave superconductivity for

10<{r}_{s}<35

and

s

-wave superconductivity for

{r}_{s}>35

This article gives a fairly detailed survey of some of the problems raised when the interaction energy fσσ'kk' between 2 fermionic quasiparticles (in 2 dimensions) is singular when

|\underline{k}-\underline{k}'|\to 0

. Before dealing with singular interactions, it is shown how a non-singular fσσ'kk' leads to a 2-dimensional Fermi liquid theory, which is internally consistent, at least as far as its infrared properties are concerned. The quasiparticle properties are calculated in detail. The question of whether singular interactions arise for the dilute Fermi gas, with short-range repulsive interactions, is investigated perturbatively. One finds a weak singularity in fσσ'kk', when the dimensionality D = 2, but it does not destabilize the Fermi liquid. A more sophisticated analysis is then given, to all orders in the interaction, using the Lippman-Schwinger equation as well as a phase shift analysis for a finite box. The conclusion is that any breakdown of Fermi liquid theory must come from non-perturbative effects. An examination is then made of some of the consequences arising if a singular interaction is introduced — the form proposed by Anderson is used as an example. A hierarchy of singular terms arise in all quantities — this is shown for the self-energy, and also the 3–point and 4–point scattering functions. These may be summed in a perfectly consistent manner. Most attention is given to the particle-hole channel, since it appears to lead to results different from those of Anderson. Nevertheless it appears that it is possible to derive a sensible theory starting from a singular effective Hamiltonian — although Fermi Liquid theory breaks down, all fermionic quantities may be calculated consistently. Finally, the effect of a magnetic field (which cuts off the infrared divergences) is investigated, and the de Haas-van Alphen amplitude calculated, for such a singular Fermionic system.