Presence versus absence of Two-Dimensional Fermi Surface Anomalies

TL;DR

This paper theoretically analyzes how Fermi surface anomalies manifest differently in two-dimensional versus three-dimensional electron systems, focusing on temperature-dependent effective mass corrections for various interactions.

Contribution

It provides analytical results showing the absence of Fermi surface anomalies in 2D electron-phonon interactions and the presence of anomalies in electron-paramagnon and electron-electron interactions, contrasting with 3D systems.

Findings

2D electron-phonon interactions yield no Fermi surface anomaly, with T^2 correction.

Electron-paramagnon and electron-electron interactions in 2D show T correction, indicating anomalies.

Comparison of specific heat behavior between 2D and 3D Fermi systems.

Abstract

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 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 $\mathcal{O}(T^2)$ temperature correction and thus remaining consistent with the Sommerfeld expansion of the non-interacting Fermi function, in contrast to the corresponding 3D situation where the temperature correction to the renormalized effective mass has the anomalous $T^2 \log T$ behavior. By contrast, both electron-paramagnon and electron-electron interactions lead to the anomalous $\mathcal{O}(T)$ corrections to the 2D effective mass renormalization in contrast to $T^2 \log T$ behavior in the corresponding 3D interacting systems. We provide detailed analytical results, and comment on the conditions under which a $T^2 \log T$ 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.