1. Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK
2. Institute for Microelectronics Technology, 142432 Chernogolovka, Russia
3. Institute for Molecules and Materials, Radboud University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands

Correspondence to: K. S. Novoselov¹A. K. Geim¹ Correspondence and requests for materials should be addressed to A.K.G. (Email: geim@man.ac.uk) or K.S.N. (Email: kostya@man.ac.uk).

Abstract

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry^{1, 2, 3}. The ideas underlying quantum electrodynamics also influence the theory of condensed matter^{4, 5}, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon^{6, 7}) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c_* 10⁶ m s^-1. Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m_c of massless carriers in graphene is described by E = m_cc_*². This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

1. Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK
2. Institute for Microelectronics Technology, 142432 Chernogolovka, Russia
3. Institute for Molecules and Materials, Radboud University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands

Correspondence to: K. S. Novoselov¹A. K. Geim¹ Correspondence and requests for materials should be addressed to A.K.G. (Email: geim@man.ac.uk) or K.S.N. (Email: kostya@man.ac.uk).

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