Topological basis for understanding the behavior of the heavy-fermion metal $\rm {\beta-YbAlB_4}$ under application of magnetic field and pressure

TL;DR

This paper provides a topological explanation for the robust non-Fermi-liquid behavior of the heavy-fermion metal $ m eta-YbAlB_4$ under magnetic field and pressure, using fermion-condensation theory to explain experimental scaling laws and phase diagrams.

Contribution

It introduces a topological framework based on fermion-condensation theory to explain the NFL behavior and scaling laws in $ m eta-YbAlB_4$, without relying on quantum critical fluctuations.

Findings

NFL behavior remains robust under pressure in zero magnetic field

Scaling laws are consistent with fermion-condensation theory

Paramagnetic NFL phase occurs without magnetic criticality

Abstract

Informative recent measurements on the heavy-fermion metal $\rm \beta-YbAlB_4$ 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.