# Dimensional reduction, quantum Hall effect and layer parity in graphite films

## TL;DR

This paper reports the observation of the quantum Hall effect in thick graphite films, revealing a dimensional reduction of electron dynamics and a layer parity-dependent valley polarization, with implications for understanding 2D and 3D electron systems.

## Contribution

It demonstrates quantum Hall effects in thick graphite, showing how high magnetic fields induce dimensional reduction and how layer parity affects valley polarization and electron interactions.

## Key findings

- Quantum Hall effect observed in graphite up to hundreds of layers.
- Layer parity influences valley polarization and QHE gap sizes.
- Signatures of electron-electron interactions, including fractional QHE.

## Abstract

The quantum Hall effect (QHE) originates from discrete Landau levels forming in a two-dimensional (2D) electron system in a magnetic field. In three dimensions (3D), the QHE is forbidden because the third dimension spreads Landau levels into multiple overlapping bands, destroying the quantisation. Here we report the QHE in graphite crystals that are up to hundreds of atomic layers thick - thickness at which graphite was believed to behave as a 3D bulk semimetal. We attribute the observation to a dimensional reduction of electron dynamics in high magnetic fields, such that the electron spectrum remains continuous only in the direction of the magnetic field, and only the last two quasi-one-dimensional (1D) Landau bands cross the Fermi level. In sufficiently thin graphite films, the formation of standing waves breaks these 1D bands into a discrete spectrum, giving rise to a multitude of quantum Hall plateaux. Despite a large number of layers, we observe a profound difference between films with even and odd numbers of graphene layers. For odd numbers, the absence of inversion symmetry causes valley polarisation of the standing-wave states within 1D Landau bands. This reduces QHE gaps, as compared to films of similar thicknesses but with even layer numbers because the latter retain the inversion symmetry characteristic of bilayer graphene. High-quality graphite films present a novel QHE system with a parity-controlled valley polarisation and intricate interplay between orbital, spin and valley states, and clear signatures of electron-electron interactions including the fractional QHE below 0.5 K.

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Source: https://tomesphere.com/paper/1812.10740