Local moments and the Kondo effect

Abstract

Strongly correlated electrons One of the fascinating growth areas in condensed matter physics concerns strongly correlated systems : states of matter in which the many-body interaction energies dominate the kinetic energies, becoming large enough to qualitatively transform the macroscopic properties of the medium. The growing list of strongly correlated systems includes the following: • Cuprate superconductors , where interactions among electrons in localized 3 d -shells form an antiferromagnetic Mott insulator , which develops high-temperature superconductivity when doped • Heavy-electron compounds , in which localized magnetic moments immersed within the metal give rise to electron quasiparticles with effective masses in excess of a thousand bare-electron masses • Fractional quantum Hall systems , where strong interactions in the lowest Landau level of a two-dimensional electron fluid generate an incompressible state with quasiparticles of fractional charge and statistics • Quantum dots , which are tiny pools of electrons in semiconductors that act as artificial atoms. As the gate voltage is changed, the electron repulsion in the dot causes a Coulomb blockade , whereby electrons can only be added one-by-one to the quantum dot • Cold atomic gases , in which the interactions between neutral atoms governed by twobody resonances can be magnetically tuned to create a whole new world of strongly correlated quantum fluids. In each case, the electron system has been tuned – by electronic or nuclear chemistry, by geometry or nanofabrication, to give rise to a quantum state with novel collective properties, in which the interactions between the particles are large compared with their kinetic energies. The next three chapters will introduce one corner of this field: the physics of local moments and heavy-fermion compounds. A large class of strongly correlated materials have atoms with partially filled d - or f -orbitals. Heavy-electron materials are an extreme example, in which one component of the electron fluid is highly localized, usually inside f -orbitals, giving rise to the formation of magnetic moments. The interaction of localized magnetic moments with the conduction sea provides the driving force for the strongly correlated electron physics in these materials.