Quantum Criticality without Tuning in the Mixed Valence Compound   beta-YbAlB4
  Fermi liquid theory, the standard theory of metals, has been challenged by a number of observations of anomalous metallic behavior found in the vicinity of a quantum phase transition. The breakdown of the Fermi liquid is accomplished by fine-tuning the material to a quantum critical point using a control parameter such as the magnetic field, pressure, or chemical composition. Our high precision magnetization measurements of the ultrapure f-electron based superconductor {\beta}-YbAlB4 demonstrate a scaling of its free energy indicative of zero-field quantum criticality without tuning in a metal. The breakdown of Fermi-liquid behavior takes place in a mixed-valence state, in sharp contrast with other known examples of quantum critical f-electron systems that are magnetic Kondo lattice systems with integral valence. 
Yosuke Matsumoto, Satoru Nakatsuji, Kentaro Kuga, Yoshitomo Karaki,   Naoki Horie, Yasuyuki Shimura, Toshiro Sakakibara, And...
cond-mat.str-el