Interaction-induced enhancement of $g$-factor in graphene

TL;DR

This paper investigates how electron interactions and impurities affect the $g$-factor in graphene under magnetic fields, revealing oscillations and impurity-induced suppression, with implications for experimental observations.

Contribution

It demonstrates the interaction-induced enhancement and oscillation of the $g$-factor in graphene, and how substrate impurities suppress these effects, providing new insights into spin properties.

Findings

$g$-factor is enhanced and oscillates with filling factor $ u$

Impurities suppress $g$-factor oscillations

High impurity levels lead to a $g^{ ext{*}} o 2.3$ saturation

Abstract

We study the effect of electron interaction on the spin-splitting and the $g$-factor in graphene in perpendicular magnetic field using the Hartree and Hubbard approximations within the Thomas-Fermi model. We found that the $g$-factor is enhanced in comparison to its free electron value $g=2$ and oscillates as a function of the filling factor $\nu $ in the range $2\leq g^{\ast}\lesssim 4$ reaching maxima at even $\nu $ and minima at odd $\nu $. We outline the role of charged impurities in the substrate, which are shown to suppress the oscillations of the $g^{\ast}$-factor. This effect becomes especially pronounced with the increase of the impurity concentration, when the effective $g$-factor becomes independent of the filling factor reaching a value of $g^{\ast}\approx 2.3$. A relation to the recent experiment is discussed.