Thermal smearing of the magneto-Kohn anomaly for Dirac materials and comparison with the two-dimensional electron liquid

TL;DR

This paper investigates how magnetic fields and temperature influence the static polarization functions in monolayer graphene and 2D electron liquids, revealing significant differences in screening effects relevant to low-dimensional physics.

Contribution

It provides a comprehensive numerical comparison of magnetic and thermal effects on polarization in graphene and 2DEL, correcting previous analytic flaws and highlighting differences in screening behaviors.

Findings

Distinct screening behaviors for graphene and 2DEL.

Identification of flaws in previous analytic derivations.

Implications for Kohn anomaly and Friedel oscillations.

Abstract

We compute and compare the effects due to a uniform perpendicular magnetic field as well as temperature on the static polarization functions for monolayer graphene (MLG), associated with the Dirac point, with that for the two-dimensional electron liquid (2DEL) with the use of comprehensive numerical calculations. Previous results for the 2DEL are discussed and, in particular, we point out a flaw in a reported analytic derivation which was carried out to exhibit the smearing of the Fermi surface for 2DEL. The relevance of our study to the Kohn anomaly in low-dimensional structures and the Friedel oscillations for the screening of the potential for a dilute distribution of impurities is reported. Our results show substantial differences due to screening for the 2DEL and MLG which have not been given adequate attention previously.