Unconventional Quantum Criticality in Heavy-Fermion Compounds

We review magnetic quantum-critical points (QPCs) in heavy-fermion compounds separating at zero temperature: an antiferromagnetically ordered state and a nonordered ground state. At the magnetic instability, the Fermi-liquid (FL) description valid for normal metals breaks down, giving rise to unusual, non-Fermi-liquid (NFL) low-temperature behavior. After a short introduction to phase transitions and to T = 0 phase transitions in general as well as to the physics of heavy-fermion systems, the two main theoretical scenarios describing the physics at QPCs in these systems are presented, the conventional spin-density-wave (SDW) scenario and the unconventional Kondo-breakdown scenario. Whereas for the conventional scenario experimental data for CeCu2Si2 and Ce1−xLaxRu2Si2 are discussed only briefly, we focus in more detail on the unusual behavior of CeCu6−xAux and YbRh2Si2 at their respective QPCs and show that these systems are best described within the unconventional scenario.