Fragile versus stable two-dimensional fermionic quasiparticles

TL;DR

This paper theoretically investigates the robustness of Fermi liquid quasiparticles in a two-dimensional electron gas with Coulomb interactions, revealing conditions under which quasiparticles remain stable or become fragile due to collective plasmon coupling.

Contribution

It provides a detailed analysis of quasiparticle stability in 2D electron gases, highlighting the emergence of non-Fermi liquid behavior near a critical wave vector due to plasmon interactions.

Findings

Quasiparticles are stable up to high energies in 2D electron gas.

Fragile quasiparticle behavior occurs near a critical wave vector.

Coupling with plasmon modes causes deviations from Fermi liquid theory.

Abstract

We provide a comprehensive theoretical investigation of the Fermi liquid quasiparticle description in two-dimensional electron gas interacting via the long-range Coulomb interaction by calculating the electron self-energy within the leading-order approximation, which is exact in the high-density limit. We find that the quasiparticle energy is larger than the imaginary part of the self-energy up to very high energies, implying that the basic Landau quasiparticle picture is robust up to far above the Fermi energy. We find, however, that the quasiparticle picture becomes fragile in a small discrete region around a critical wave vector where the quasiparticle spectral function strongly deviates from the expected quasiparticle Lorentzian line shape with a vanishing renormalization factor. We show that such a non-Fermi liquid behavior arises due to the coupling of quasiparticles with the collective plasmon mode. This situation is somewhat intermediate between the one-dimensional interacting electron gas (i.e., Luttinger liquid), where the Landau Fermi liquid theory completely breaks down since only bosonic collective excitations exist, and three-dimensional electron gas, where quasiparticles are well-defined and more stable against interactions than in one and two dimensions. We use a number of complementary definitions for a quasiparticle to examine the interacting spectral function, contrasting two-dimensional and three-dimensional situations critically.