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. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) 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* approximately 10(6) 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(c)c*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.

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Two-dimensional gas of massless Dirac fermions in graphene

A review of dielectric data for a wide range of solids proves the existence of a remarkable ‘universality’ of frequency and time responses which is essentially incompatible with the multiplicity of currently accepted detailed interpretations. Certain unique features of the universal behaviour strongly suggest the dominant role of many-body interactions.

The ‘universal’ dielectric response

A brief description is given of the various manifestations of the universal fractional power law relaxation processes, which are contrasted with the classical or Debye law. It is shown that the universal law is indeed found in a remarkable variety of physical and chemical situations, and this is deemed to merit a special attempt at finding a suitably general theoretical model. Several such models are briefly described, and a novel very general approach based on the so-called energy criterion is introduced. It is concluded that it is not yet possible to establish with certainty the validity of any of the models. >

The universal dielectric response

We consider an Ising model in which the spins are coupled by infinite-ranged random interactions independently distributed with a Gaussian probability density. Both "spinglass" and ferromagnetic phases occur. The competition between the phases and the type of order present in each are studied.

Solvable Model of a Spin-Glass

Graphene based materials: Past, present and future

1. Introduction 2. Theory of Electrons in a Non-Crystalline Medium 3. Phonons and Polarons 4. The Fermi Glass and the Anderson Transition 5. Liquid Metals and Semimetals 6. Non-Crystalline Semiconductors 7. Tetrahedrally-Bonded Semiconductors - Amorphous Germanium and Silicon 8. Aresnic and Other Three-Fold Co-ordinated Materials 9. Chalcogenide and Other Glasses 10. Selenium, Tellurium, and their Alloys

Electronic processes in non-crystalline materials

The experimental evidence concerning the density of states in amorphous semiconductors and the ranges of energy in which states are localized is reviewed; this includes d.c. and a.c. conductivity, drift mobility and optical absorption. There is evidence that for some chalcogenide semiconductors the model proposed by Cohen, Fritzsche and Ovshinsky (1969) should be modified by introducing a band of localized states, near the centre of the gap. The values of C, when the d.c. conductivity is expressed as C exp (- E/kT), are considered. The behaviour of the optical absorption coefficient near the absorption edge and its relation to exciton formation are discussed. Finally, an interpretation of some results on photoconductivity is offered.

Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors

To mark the 100th anniversary of the publication of Lord Rutherford's paper in Philosophical Magazine on the nuclear model of the atom, we review his ground-breaking work and outline subsequent developments.

Commentary on ‘The scattering of α and β particles by matter and the structure of the atom’ by E. Rutherford (Philosophical Magazine 21 (1911) 669–688)

E. A. Davis

Papers

Electronic processes in non-crystalline materials

Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors

Commentary on ‘The scattering of α and β particles by matter and the structure of the atom’ by E. Rutherford (Philosophical Magazine 21 (1911) 669–688)