J. Phys. IV France
Volume 116, October 2004
Page(s) 171 - 201

J. Phys. IV France 116 (2004) 171-201

DOI: 10.1051/jp4:2004116006

Vortex matter in two dimensions: An introduction from a solid state physics viewpoint

B. Douçot

Laboratoire de Physique Théorique et Hautes Énergies, CNRS UMR 7589, Universités Paris VI and VII, 4 place Jussieu, 75252 Paris Cedex 05, France

Motivated by possible applications to cold atomic gases in a rotating trap, we give an overview of some important concepts in two-dimensional vortex physics. In the context of Josephson junction arrays, we first discuss the crucial role played by vortices in both the thermal superconducting to normal metal transition, and the zero temperature superconducting to Mott insulator transition. Important notions on vortex dynamics in these arrays are then presented, with emphasis on experimental results indicating the quantum nature of vortex motion at low temperature. We move then to the Fractional Quantum Hall effect, as observed in electronic systems, and introduce the notions of fractional excitations, generalized statistics, and composite fermions, which have played a key role in the theoretical description of this remarkable phenomenon. Very likely, cold atomic gases in a rotating trap will soon provide a way to explore the bosonic version of the Fractional Quantum Hall effect, and thus shedding new light on these subtle strongly correlated quantum fluids.

© EDP Sciences 2004