4. - Quantum Hall Effect in Graphene

Summary

Introduction

Graphene is formed of C atoms. C is an element in the IV^th column of the periodic table and has four valence electrons in the outermost shell. It can make two types of chemical bonds, namely sp³, which results in diamond known from ancient times, and a more stable sp², which results in graphite that is known for the last 500 years. A quick look at the discoveries of different allotropes of C is available in Table 4.1. The sp² hybridization causes planar configuration involving 3 of the 4 electrons, which are 120° apart and are bound by σ bonds that add stiffness (and flatness too) to the linkage between the C–C atoms, while the fourth electron bound to the C atoms via the π bond projects out of the plane, and is available for conduction. Thus, the electronic structure that we shall be discussing elaborately is due to these π electrons.

Graphene was the first discovery of atomically thin perfect two-dimensional (2D) material. Andre Geim and co-workers successfully exfoliated graphene from graphite [2, 3]. Some of the remarkable properties of graphene (which, unfortunately, we shall not worry too much about) include its strength, impermeability, very large thermal conductivity (at least one order larger than copper), as a molecule sensor, transparent (for its usage in displays), in the field of biology, such as neuron growth and DNA sequencing, and many more. Owing to the tremendous fundamental and technological applications of graphene, the discovery earned a Nobel Prize to A. Geim and K. Novoselov, both from the University of Manchester in the UK in 2010.