Persistent Friedel oscillations in Graphene due to a weak magnetic field

Two opposite chiralities of Dirac electrons in a 2D graphene sheet modify strongly the Friedel oscillations: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. 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. Moreover, in this interval, the field-dependent oscillations do not decay with distance. This effect originates from the magnetic-field-induced chiral symmetry breaking near the Dirac point and implies anomalous sensitivity of the interaction effects in graphene and graphene-based heterostructures to a weak non-quantizing magnetic field.