Persistent Friedel oscillations in graphene due to a weak magnetic field

Abstract

Two opposite chiralities of Dirac electrons in a two-dimensional (2D) graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/{r}^{3}$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is dominant in a parametrically large spatial interval ${p}_{0}^{\ensuremath{-}1}\ensuremath{\lesssim}r\ensuremath{\lesssim}{k}_{F}{l}^{2}$, where $l$ is the magnetic length, ${k}_{F}$ is Fermi momentum, and ${p}_{0}^{\ensuremath{-}1}={({k}_{F}l)}^{4/3}/{k}_{F}$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.