SALLE INHABITUELLE: salle de séminaire de l'INSP tour 22-23 salle 317 (3ème étage).

Lara Benfatto (CNR et Université de Rome Sapienza)

Berezinskii-Kosterlitz-Thouless transition in 2D superconductors

Lecture I: The Beresinskii-Kosterlitz-Thouless transition: the two-dimensional world and its peculiarities
More than 40 years after the seminal work by Berezinskii, Kosterlitz and Thouless the
BKT transition remains one of the most spectacular phenomena in condensed matter
systems, as it has been acknowledged by the 2016 Nobel Prize. Even though it was originally formulated within the context of the two dimensional XY model for classical spins, it represents the paradigm for the superfluid transition in two dimensions. As such, it has been the subject of an intense theoretical and experimental investigation in a variety of systems, ranging from thin films of superconductors to artificial heterostructures and cold atoms.
In the first lecture I will give an introduction to the basic mathematical ingredients needed to understand the occurrence of a BKT transition within the context of the classical 2D XY model. After discussing the difference between order and rigidity for a second-order phase transition, I will discuss the peculiar role of vortices in 2D and I will derive the mapping onto the Coulomb-gas model. Finally, I will sketch the main outcomes of the renormalization-group approach for the BKT phase transition.

Lecture II: Applications to superfluids. What we should expect to see in real systems?
The Beresinskii-Kosterlitz-Thouless transition is expected to describe the metal-to-superconductor thermal transition in quasi-2D systems. However, despite many efforts along the years its signatures remain rather elusive. In this second lectures I will give an overview of the numerous attempts we made along the years to identify the mechanisms which may hinder a clear-cut observation of BKT physics in 2D films of conventional and unconventional superconductors. In particular I will discuss the role of the vortex-core energy and of the spontaneous inhomogeneity of the superconducting background which naturally emerge in disordered thin films. These effects must be seriously taken into account while addressing the famous universal jump of the superfluid density, the non-linear IV characteristics near Tc, or the paraconductivity effects while approaching it from above. Finally, I will make a comparison with some recent results within the context of cold atoms, underlying differences and analogies between the two classes of systems.