Persistent Friedel oscillations in Graphene due to a weak magnetic field

Ke Wang, M. E. Raikh, T. A. Sedrakyan

Published 2020-07-27Version 1

Two opposite chiralities of Dirac electrons in a 2D graphene sheet strongly modify Friedel oscillations: the electrostatic potential around a single, non-magnetic impurity in graphene decays much faster than in 2D electron gas. In the semiclassical regime, $k_F r\gg 1$, where $k_F$ is the Fermi momentum, and $r$ is the distance from the impurity, it behaves as $\sim\cos(2k_Fr)/r^3$. Here we show that the weak uniform magnetic field affects Friedel oscillations in an anomalous way. It breaks the chiral symmetry of Dirac electrons and generates {\em dominant}, field-dependent oscillations that do not decay with distance in a parametrically large spatial interval $p_0^{-1}\lesssim r\lesssim k_Fl^2$, where $l$ is the magnetic length, and $p_0^{-1}=(k_Fl)^{4/3}/k_F$. This effect originates from chiral symmetry breaking near a Dirac point and implies anomalous sensitivity of interaction-induced effects in graphene and graphene-based heterostructures to the weak non-quantizing magnetic field.