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Journal of the Physical Society of Japan

Anomalous Damping of Quasiparticles in Two-Dimensional Fermi Systems

Satoshi Fujimoto

Published Jul 15, 1990• 20 citations
Publisher

Abstract

We report an anomalous property of two-dimensional Fermi systems. The damping of quasiparticles in the conventional Fermi liquid is proportional to T 2 . This is altered in low-dimensional systems. In two dimensions, anomalous T -dependence of the damping, T 2 ln T , is obtained by the Fermi liquid analysis. However, the Fermi liquid description can be constructed consistently, in contrast to the one-dimensional systems.

DOI
10.1143/jpsj.59.2316

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We report an anomalous property of two-dimensional Fermi systems. The damping of quasiparticles in the conventional Fermi liquid is proportional to T 2 . This is altered in low-dimensional systems. In two dimensions, anomalous T -dependence of the damping, T 2 ln T , is obtained by the Fermi liquid analysis. However, the Fermi liquid description can be constructed consistently, in contrast to the one-dimensional systems.
This Letter addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis provides a further insight into the nature and properties of the collective bosonic modes in such systems.
We theoretically consider Fermi surface anomalies manifesting in the temperature-dependent quasiparticle properties of two-dimensional (2D) interacting electron systems, comparing and contrasting with the corresponding three-dimensional (3D) Fermi liquid situation. In particular, employing microscopic many-body perturbative techniques, we obtain analytically the leading-order and the next-to-leading-order interaction corrections to the renormalized effective mass for three distinct physical interaction models: electron-phonon, electron-paramagnon, and electron-electron Coulomb coupling. We find that the 2D renormalized effective mass does not develop any Fermi surface anomaly due to electron-phonon interaction, manifesting O(T2)\mathcal{O}({T}^{2})O(T2) temperature correction and thus remaining consistent with the Sommerfeld expansion of the noninteracting Fermi function, in contrast to the corresponding 3D situation where the temperature correction to the renormalized effective mass has the anomalous T2logT{T}^{2}logTT2logT behavior. In contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous O(T)\mathcal{O}(T)O(T) corrections to the 2D effective mass renormalization in contrast to T2logT{T}^{2}logTT2logT behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a T2logT{T}^{2}logTT2logT term could possibly arise in the 2D quasiparticle effective mass from electron-phonon interactions. We also compare results for the temperature-dependent specific heat in the interacting 2D and 3D Fermi systems, using the close connection between the effective mass and specific heat.
This note addresses the problem of constructing a proper bosonized description of the collective modes in strongly interacting (non-)Fermi liquids which is specific to two spatial dimensions. Although, in a mild form, this subtlety exists in the Fermi liquid as well, the discussion focuses on the effects of long-ranged and/or retarded interactions which can completely destroy the fermionic quasiparticles. The present analysis also provides a further insight into the nature and properties of the collective bosonic modes in such systems.
We examine the validity of Fermi-liquid theory in the low-density two-dimensional Hubbard model. From the ground-state energy we obtain the quasiparticle energy and the Landau interaction function. Then we prove that the quasiparticle-interaction function is finite and that the quasiparticle residue is nonzero for repulsive interactions. We also find, as a function of the excitation energy \ensuremath{\epsilon}, that the quasiparticle lifetime \ensuremath{\sim}1/${\mathrm{\ensuremath{\epsilon}}}^{2}$ln\ensuremath{\epsilon}. Hence, we conclude that Fermi-liquid theory holds in our model.
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.