Measurable lattice effects on the charge and magnetic response in graphene

TL;DR

This paper investigates how lattice effects influence the magnetic susceptibility and charge oscillations in doped graphene, revealing paramagnetism and anisotropic Friedel oscillations beyond the Dirac cone approximation.

Contribution

It provides an exact tight-binding expression for graphene's magnetic susceptibility and analytically characterizes lattice-induced anisotropic Friedel oscillations.

Findings

Graphene exhibits orbital paramagnetism over various doping levels.

Lattice effects restore regular 2D Friedel oscillations with sixfold anisotropy.

Explicit formulas for charge response considering lattice effects are derived.

Abstract

The simplest tight-binding model is used to study lattice effects on two properties of doped graphene: i) magnetic orbital susceptibility and ii) regular Friedel oscillations, both suppressed in the usual Dirac cone approximation. i) An exact expression for the tight-binding magnetic susceptibility is obtained, leading to orbital paramagnetism in graphene for a wide range of doping levels which is relevant when compared with other contributions. ii) Friedel oscillations in the coarse-grained charge response are considered numerically and analytically and an explicit expression for the response to lowest order in lattice effects is presented, showing the restoration of regular 2d behavior, but with strong sixfold anisotropy.