Two-dimensional gas of massless Dirac fermions in graphene

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 Schr?dinger 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.     

Non-quantized penetration of magnetic field in the vortex state of superconductors

As first pointed out by Bardeen and Ginzburg in the early sixties, the amount of magnetic flux carried by vortices in superconducting materials depends on their distance from the sample edge, and can be smaller than one flux quantum, phi0 = h/2e (where h is Planck's constant and e is the electronic charge). In bulk superconductors, this reduction of flux becomes negligible at submicrometre distances from the edge, but in thin films the effect may survive much farther into the material. But the effect has not been observed experimentally, and it is often assumed that magnetic field enters type II superconductors in units of phi0. Here we measure the amount of flux introduced by individual vortices in a superconducting film, finding that the flux always differs substantially from phi0. We have observed vortices that carry as little as 0.001phi0, as well as 'negative vortices', whose penetration leads to the expulsion of magnetic field. We distinguish two phenomena responsible for non-quantized flux penetration: the finite-size effect and a nonlinear screening of the magnetic field due to the presence of a surface barrier. The latter effect has not been considered previously, but is likely to cause non-quantized penetration in most cases.     

Subatomic movements of a domain wall in the Peierls potential

The discrete nature of crystal lattices plays a role in virtually every material property. But it is only when the size of entities hosted by a crystal becomes comparable to the lattice period--as occurs for dislocations, vortices in superconductors and domain walls--that this discreteness is manifest explicitly. The associated phenomena are usually described in terms of a background Peierls 'atomic washboard' energy potential, which was first introduced for the case of dislocation motion in the 1940s. This concept has subsequently been invoked in many situations to describe certain features in the bulk behaviour of materials, but has to date eluded direct detection and experimental scrutiny at a microscopic level. Here we report observations of the motion of a single magnetic domain wall at the scale of the individual peaks and troughs of the atomic energy landscape. Our experiments reveal that domain walls can become trapped between crystalline planes, and that they propagate by distinct jumps that match the lattice periodicity. The jumps between valleys are found to involve unusual dynamics that shed light on the microscopic processes underlying domain-wall propagation. Such observations offer a means for probing experimentally the physics of topological defects in discrete lattices--a field rich in phenomena that have been subject to extensive theoretical study.