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 $\textit{r}$ 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 $p^{–1}_0 ≲ r ≲ k_Fl^2$, where $\textit{l}$ is the magnetic length, $k_F$ is Fermi momentum, and $p^{–1}_0 = (k_Fl)^{4/3} /k_F$. 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. Further, the obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.