Theory of the Three Dimensional Quantum Hall Effect in Graphite

TL;DR

This paper predicts a three-dimensional quantum Hall effect in graphite under high magnetic fields, characterized by quantized Hall conductivity and chiral surface states, with specific critical magnetic field estimates.

Contribution

It introduces the theoretical prediction of a 3D quantum Hall effect in graphite, analyzing the Hofstadter spectrum and surface states in a realistic model.

Findings

Quantized Hall conductivity at 04e^2/83; with c-axis lattice constant

Critical magnetic field estimated at 15.4 T for electrons

Chiral surface states enable Hall transport in the bulk

Abstract

We predict the existence of a three dimensional quantum Hall effect plateau in a graphite crystal subject to a magnetic field. The plateau has a Hall conductivity quantized at $\frac{4e^2}{\hbar} \frac{1}{c_0} $ with $c_0$ the c-axis lattice constant. We analyze the three-dimensional Hofstadter problem of a realistic tight-binding Hamiltonian for graphite, find the gaps in the spectrum, and estimate the critical value of the magnetic field above which the Hall plateau appears. When the Fermi level is in the bulk Landau gap, Hall transport occurs through the appearance of chiral surface states. We estimate the magnetic field necessary for the appearance of the three dimensional quantum Hall Effect to be $15.4 $T for electron carriers and $7.0 $T for hole carriers.