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

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.