Universal Behavior of the Heavy-Fermion Metal $$\mathrm {\beta -YbAlB_4}$$

Abstract

In this chapter, we reveal and explain a universal scaling behavior of the heavy-fermion metal \(\mathrm {\beta -YbAlB_4}\). Informative measurements on the heavy-fermion metal \(\mathrm{\beta -YbAlB_4}\) performed with applied magnetic field and pressure as control parameters are analyzed with the goal of establishing a convincing theoretical explanation for the inferred scaling laws and non-Fermi liquid (NFL) behavior, which demonstrate some unexpected features. Most notably, the robustness of the NFL behavior of the thermodynamic properties and of the anomalous \(T^{3/2}\) temperature dependence of the electrical resistivity under applied pressure P in zero magnetic field B is at variance with the fragility of the NFL phase under application of a field. We show that a consistent topological basis for this combination of observations, as well as the empirical scaling laws, may be found within fermion-condensation theory in the emergence and destruction of a flat band, and explain that the paramagnetic NFL phase takes place without magnetic criticality, thus not from quantum critical fluctuations. Schematic \(T-B\) and \(T-P\) phase diagrams are presented to illuminate this scenario.