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The Kondo lattice model (KLM) is the simplest model to describe heavy fermion materials based on Lanthanide intermetallics. The physical properties have been anticipated since the early eighties, but only in the recent years we have become able to investigate it in a comprehensive way usingthe dynamical mean-field approach (DMFA).
In my lecture, I will show you how the heavy electron state develops and its signatures in dynamical and static properties. Since the KLM contains local magnetic moments, one will expect magnetic ordering to occur. While this statement is almost evident, the precise nature of the magnetic states to be expected is less clear, and here the DMFA can give at least qualitative ideas, if not also reasonable numbers for critical temperatures or model parameters. I will indeed show you that one has an unexpectedly rich zoo of magnetic phases, which also incorporate heavy fermion magnets competing with local moment ones.
Finally, heavy fermion superconductivity is a old problem and still not resolved. We recently found a rather astonishing superconducting solution in the KLM within DMFA, which I will present to you.
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