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arXiv:cond-mat/0101417

Two-dimensional Fermi Gas Revisited

Philip Warren Anderson

Published Jan 26, 2001• 1 citation
arXivHTMLPDF

Abstract

A number of authors have taken issue with the demonstration that the 2D Fermion gas with short-range repulsive interactions (and, of course, including spin) cannot be consistently treated as a renormalised quasiparticle system. This paper shows that the arguments given in some of these papers are invalid or irrelevant.
DOI
10.48550/arxiv.cond-mat/0101417

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The authors provide a comprehensive theoretical investigation of the validity of the Fermi-liquid quasiparticle description in a two-dimensional electron gas interacting via the long-range Coulomb interaction. Contrary to popular belief, they find that quasiparticles are robust far above the Fermi momentum, perhaps providing a clue as to why the energy-band description works well far from the Fermi surface. The authors also find that there exists a small region around a critical wave vector where the quasiparticles become fragile due to their coupling to the collective modes. They also provide three-dimensional results.
We study the dilute-gas expansion for a two-dimensional Fermi system with arbitrary short-range repulsive interactions. In contrast with the three-dimensional case, we find an unusual pole in the vertex part in the particle-particle channel, for all center-of-mass momenta q2kF{\mathit{k}}_{\mathit{F}}kF​. We show that this represents an excitation consisting of bound hole pairs, which disperses down to zero energy at q=2kF{\mathit{k}}_{\mathit{F}}kF​. We study the effect of these bound states on the single-particle self-energy and find that the quasiparticles are well defined. Thus in the low-density regime, there is no breakdown of Fermi-liquid theory. In the Appendix we discuss the two-particle phase shift in the dilute Fermi gas, its connection with bound states, and the analogy with the potential scattering phase shift.
"This thesis is divided into two parts. The first describes a study of the dilute Fermi gas with short range repulsive interactions in 2D, with special emphasis on questions related to the validity of Fermi liquid theory. We find that despite the existence of non-perturbative effects due to two-dimensionality, namely linearly dispersing excitations of ""bound"" holes, the system remains in a Fermi liquid state. The quasi-particles are both long lived and weakly interacting. We also provide a microscopic calculation of the Fermi liquid parameters which determine the response functions in the standard way."
Whether a spin-1/2 Fermi gas will become ferromagnetic as the strength of repulsive interaction increases is a long-standing controversial issue. Recently this problem has been studied experimentally by Jo et al. [Science 325, 1521 (2009)] in which the authors claim a ferromagnetic transition is observed. This work is to point out the results of this experiment cannot distinguish whether the system is in a ferromagnetic state or in a nonmagnetic but strongly short-range correlated state. A conclusive experimental demonstration of ferromagnetism relies on the observation of ferromagnetic domains.
We study a two-dimensional Fermi gas with an arbitrary short-range repulsive interaction. We show that the vertex part has an unusual singularity in the particle-particle channel for all momenta q2kF{\mathit{k}}_{\mathit{F}}kF​, which is not found in higher dimensions. We interpret this as a collective mode representing a bound excitation of two holes. This mode, however, does not lead to an instability, or to a breakdown of Fermi-liquid theory in the low-density limit. The resulting Fermi-surface phase shift vanishes, and a \ensuremath{\Vert}\ensuremath{\omega}${\mathrm{\ensuremath{\Vert}}}^{5/2}$ correction to \ensuremath{\Sigma}''(kF{\mathit{k}}_{\mathit{F}}kF​,\ensuremath{\omega}) is obtained. The 2D case is also contrasted with a similar calculation in 1D.