Two-Dimensional Gas of Massless Dirac Fermions in Graphene

TL;DR

Graphene exhibits unique electronic phenomena characteristic of 2D massless Dirac fermions, including anomalous quantum Hall effects, a minimum conductivity, and Berry phase effects, revealing relativistic-like behavior in a condensed matter system.

Contribution

This paper demonstrates that electrons in graphene behave as massless Dirac fermions, showing relativistic phenomena in a two-dimensional material, which was not previously observed in such systems.

Findings

Quantum Hall effect at half-integer filling factors

Minimum conductivity persists at zero carrier concentration

Berry phase causes a phase shift in oscillations

Abstract

Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective "speed of light" c* ~10^6m/s. Our studies of graphene - a single atomic layer of carbon - have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum e^2/h, even when carrier concentrations tend to zero; c) the cyclotron mass m of massless carriers with energy E in graphene is described by equation E =mc*^2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of pi due to Berry's phase.