Topological basis for understanding the behavior of the heavy-fermion metal $\beta -\mathrm{YbAl}{\mathrm{B}}_4$ under application of magnetic field and pressure

Abstract

Informative recent measurements on the heavy-fermion metal $\beta -\mathrm{YbAl}{\mathrm{B}}_4$ performed with applied magnetic field and pressure as control parameters are analyzed with the goal of establishing a sound 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.

6 pages, 6 figures, added references

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Cited by in corpus (8)

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• Kondo hybridization and quantum criticality in $\beta$-YbAlB${}_4$ by laser-ARPES
• Toward a topological scenario for high-temperature superconductivity of copper oxides
• Strongly correlated Fermi systems as a new state of matter
• Universal $T/B$ scaling behavior of heavy fermion compounds
• Ultra spin liquid in $\mathrm{L}{\mathrm{u}}_3\mathrm{C}{\mathrm{u}}_2\mathrm{S}{\mathrm{b}}_3{\mathrm{O}}_{14}$
• Negative ion formation in lanthanide atoms: Many-body effects