Microscopic origin of heavy-fermion phase-diagram phenomena

Identify the microscopic mechanisms responsible for the complex phase diagrams and unconventional properties of heavy-fermion materials, including non-Fermi-liquid behavior near magnetic quantum critical points and unconventional superconductivity.

Background

The paper identifies the complex phase diagram of heavy-fermion materials as a central unresolved issue. These systems may exhibit antiferromagnetic order, Kondo-screened heavy-Fermi-liquid behavior, non-Fermi-liquid properties near quantum critical points, and unconventional superconductivity. Multiple mechanisms have been proposed for the quantum-critical behavior, including massless spin fluctuations, competition between magnetic order and Kondo screening, hybridization fluctuations, and disorder, but no definitive microscopic explanation has been established.

Scanning tunneling spectroscopy and quasiparticle-interference measurements are presented as tools that can reveal the momentum structure of heavy bands, magnetic excitations, and superconducting gaps, potentially enabling progress toward resolving this problem.

References

This ``strange-metal'' behavior may indicate a Mott type AFM QCP , but this, as well as whether Mott-like AFM spin fluctuations drive the spin-triplet pairing of SC2, remain to be clarified by future microscopic studies.

— Hidden magnetic order within the pressure induced superconducting dome of UTe2  (2609.29168 - Ye et al., 24 Sep 2026) in Discussion section, paragraph beginning “Notably, both FM and AFM spin fluctuations…”

One of the key unresolved challenges in this field is to identify the microscopic mechanism giving rise to the complex phase diagram of heavy fermion materials, and their many unconventional properties.

— Theory of Scanning Tunneling Spectroscopy: from Kondo Impurities to Heavy Fermion Materials  (1701.07574 - Morr, 2017) in Section 1, Introduction

While much experimental and theoretical effort has focused on illuminating its unconventional properties, and the microscopic mechanism underlying the emergence of superconductivity, no consensus has been reached to-date.

— Theory of Scanning Tunneling Spectroscopy: from Kondo Impurities to Heavy Fermion Materials  (1701.07574 - Morr, 2017) in Section 4.2, “Differential Conductance and QPI spectroscopy in CeCoIn5”

The nature of the AFL phase remains enigmatic: On the one hand a LFL phase forms upon cooling through $T_{\rm N}(B)$ , with effective quasiparticle masses even considerably larger than those in the PFL phase , while on the other hand, AF ordering sets in with staggered moments possibly along the hard crystal-electric-field direction as tiny as $2\times10{-3}\mu_{\rm B}$/Yb .

— Evolution of electron spin resonance through a metallic quantum critical phase diagram  (2609.03994 - Scheffler et al., 3 Sep 2026) in Introduction, paragraph discussing the AFL phase

In addition, extending high-pressure studies to Ce$_5$RhGe$_2$ and Ce$_5$IrGe$_2$ will clarify whether the quantum critical behavior and superconductivity observed in Ce$_5$CoGe$_2$ represent a universal feature of this family or depend sensitively on the underlying magnetic ground state.

— Magnetic phases of Kondo lattice materials Ce$_5$RhGe$_2$ and Ce$_5$IrGe$_2$  (2609.08580 - Zhang et al., 8 Sep 2026) in Discussion and Summary

Therefore, a possible AFM QCP exists in Ce$4$Ge$_7$ around $P{\text{c} = \SI{10.2}{GPa}$. While non-Fermi-liquid behavior and divergent effective masses are commonly observed around the AFM QCP in heavy-fermion systems, the microscopic origin of such QCPs remains a central challenge in strongly correlated quantum many-body theory. Key questions include whether they arise from itinerant spin-density-wave fluctuations or from local Kondo destruction, as well as the conditions and mechanisms for unconventional superconductivity.

— Evolution of Magnetism in Ce$_4$Ge$_7$ under Magnetic Field and Pressure  (2609.37129 - Ye et al., 29 Sep 2026) in Section III.C, “Pressure-Induced Quantum Critical Behavior”