Critical vs Lowest-Landau-Level Scaling in the Ginzburg­landau Theory

Abstract

Conventional, low-T _c superconductors seen to provide archetypical examples of second-order phase transitions described by mean-field theory. In high-T _c materials. on the other hand. the critical region is much larger. so that non-classical critical behaviour may be observable. One way of investigating this is to look for scaling behaviour of the kind exhibited by magnets and fluids near their critical points. There is, however, a second kind of scaling behaviour observed in conventional type-II superconductors in the neighbourhood of the upper critical field. which results from the confinement of Cooper pairs to their lowest Landau levels in an applied magnetic field. In this talk, I will briefly review the critical properties of ferromagnets and superfluid ⁴ He and, using renormalization-group arguments. discuss the conditions under which similar behaviour might be expected in superconductors. Finally, I will suggest, on the basis of a Hartree approximation whereabouts in the phase diagram either critical or lowest-Landau-level scaling might be expected.