Abstract

A weak attractive interaction among electrons can lead to a macroscopic quantum state in which the electrons are paired. The main property of this state is to conduct electricity without dissipation. Metallic systems which exhibit it are known as superconductors. I will start by reviewing our current understanding of this phenomenon. At high magnetic fields, superconductivity can survive via the formation of inhomogeneous states. This is particularly true for the inhomogeneous superconducting state called the “Fulde-Ferrell-Larkin-Ovchnnikov” (FFLO) state. This state appears as a consequence of the finite momentum of the superconducting electron pairs. Although it has been predicted more than 40 years ago, its experimental observation has been a challenge. In the first part of my talk, I will review recent experimental results suggesting that the FFLO state is realized in a heavy fermion superconductor, CeCoIn5, with a particular emphasis on what we learn from the anisotropy of thermal conductivity about the spatial structure of the superconducting wavefunction. The second part of my talk will be devoted to the anomalous metallic state that leads to the unconventional superconductivity in CeCoIn5. I will review transport and thermodynamic evidence for an effective mass enhancement as the magnetic field approaches the superconducting upper critical field Hc2 from above. In our current understanding of heavy fermion compounds, this is attributed to a continuous ground state transformation also called a quantum phase transition. I will discuss the possible origin of a quantum phase transition close to Hc2 in CeCoIn5 and its relation to superconductivity, based on the evolution of the magnetic field phase diagram with pressure and Sn-doping.