Theory of the Room-Temperature QHE in Graphene

TL;DR

This paper explains the room-temperature quantum Hall effect in graphene using a composite boson framework, highlighting phonon-mediated attraction and Bose-Einstein condensation as key mechanisms.

Contribution

It introduces a novel explanation of the QHE in graphene based on composite bosons and phonon exchange, differing from the traditional Dirac fermion approach.

Findings

QHE arises from phonon exchange attraction near Fermi surface 'necks'

Hall plateau linked to Bose-Einstein condensation of c-bosons

High electron and hole densities due to different movement channels

Abstract

The unusual quantum Hall effect (QHE) in graphene is often discussed in terms of Dirac fermions moving with a linear dispersion relation. The same phenomenon will be explained in terms of the more traditional composite bosons, which move with a linear dispersion relation. The "electron" (wave packet) moves easier in the direction [1,1,0,c-axis] = [1,1,0] of the honeycomb lattice than perpendicular to it, while the "hole" moves easier in [0,0,1]. Since "electrons" and "holes" move in different channels, the number densities can be high especially when the Fermi surface has "necks". The strong QHE arises from the phonon exchange attraction in the neighborhood of the "neck" Fermi surfaces. The plateau observed for the Hall conductivity and the accompanied resistivity drop is due to the Bose-Einstein condensation of the c-bosons, each forming from a pair of one-electron--two-fluxons c-fermions by phonon-exchange attraction.