Quasiparticle effective mass divergence in two dimensional electron systems

TL;DR

This paper investigates the behavior of quasiparticle effective mass in 2D electron systems using RPA, revealing a divergence at a critical interaction strength, which could imply a transition at low electron densities.

Contribution

It provides the first calculation of effective mass divergence in 2D electron systems within the RPA framework, highlighting a potential phase transition at low densities.

Findings

Effective mass diverges at a critical $r_s$ (~16).

Strong increase of effective mass with increasing $r_s$.

Discussion of implications for low-density electron liquids.

Abstract

Within the infinite series of ring (or bubble) diagram approximation for the electronic self-energy as appropriate for the long-range Coulomb interaction, we calculate the density-dependent T=0 Fermi liquid quasiparticle effective mass renormalization in two dimensional (2D) electron systems in the random-phase-approximation (RPA). We find that the quasiparticle effective mass increases very strongly with increasing $r_s$, exhibiting an unexpected divergence at a critical $r_s$ value ($\sim 16$ in the ideal 2D system). We discuss the possibility for and the consequences of such an interaction induced effective mass divergence as the electron density decreases, and critically comment on the likely theoretical scenarios which could lead to such a low density effective mass divergence in electron liquids.