Persistent Friedel oscillations in Graphene due to a weak magnetic field

Two opposite chiralities of Dirac electrons in a 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 {\em dominant} in a parametrically large spatial interval \(p_0^{-1}\lesssim r\lesssim k_Fl^2\), where \(l\) is the magnetic length, \(k_F\) is Fermi momentum and \(p_0^{-1}=(k_Fl)^{4/3}/k_F\). 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.