Two-Dimensional Superfluids

Abstract

These lectures describe the behaviour of two-dimensional superfluids, which differ from three-dimensional systems in having phase transitions driven by thermally excited vortices. Firstly, I will discuss the Kosterlitz-Thouless-Berezinskii (KTB) theory of the superfluid transition in helium films, which is due to unbinding of vortex-antivortex pairs. Next, I will describe the modifications of this transition due to screening effects at the zero field transition in superconductors. The transition of a clean superconducting film in a perpendicular magnetic field, caused by melting of the flux lattice, will be discussed next. This may also be of the KTB type, involving unbinding of dislocations (with a second transition due to disclination unbinding first discussed by Halperin and Nelson) or may be first order. Finally, the case of a dirty two-dimensional superconductor in a field will be discussed. This has a vortex glass transition (analogous to the spin glass transition in magnetic systems) at zero temperature. Results of recent experiments and simulations which provide evidence for vortex glass behavior will be discussed.