Persistent Friedel oscillations in Graphene due to a weak magnetic field

TL;DR

This paper demonstrates that a weak magnetic field induces a dominant, non-decaying contribution to Friedel oscillations in graphene, significantly altering their spatial behavior due to a spin-dependent magnetic phase.

Contribution

It reveals a novel magnetic field effect on Friedel oscillations in graphene, showing a dominant, non-decaying contribution over a large spatial interval, which is a new insight into electron interactions.

Findings

Magnetic field creates a dominant, non-decaying oscillation contribution.

Oscillations decay as 1/r^3 in graphene without magnetic field.

Field-dependent effects influence transport and thermodynamics.

Abstract

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.