Angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) have become indispensable tools in the study of correlated quantum materials. Both probe complementary aspects of the single-particle excitation spectrum. Taken together, ARPES and STM have the potential to explore properties of the electronic Green’s function, a central object of many-body theory. This review explicates this potential with a focus on heavy-electron quantum criticality, especially the role of Kondo destruction. A discussion on how to probe the Kondo destruction effect across the quantum-critical point using ARPES and STM measurements is presented. Particular emphasis is placed on the question of how to distinguish between the signatures of the initial onset of hybridization-gap formation, which is the “high-energy” physics to be expected in all heavy-electron systems, and those of Kondo destruction, which characterizes the low-energy physics and, hence, the nature of quantum criticality. Recent progress and possible challenges in the experimental investigations are surveyed, the STM and ARPES spectra for several quantum-critical heavy-electron compounds are compared, and the prospects for further advances are outlined.

Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh ₂ Si ₂ , a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the quantum-critical point from a smooth background contribution; the latter exists away from the quantum-critical point and is detectable through our studies only over a wide range of magnetic field. Importantly, the width of the critical crossover is proportional to temperature, which violates the predictions of conventional theory and is instead consistent with an energy over temperature, E / T , scaling of the quantum-critical single-electron fluctuation spectrum. Our results provide evidence that the quantum-dynamical scaling and a critical Kondo breakdown simultaneously operate in the same material. Correspondingly, we infer that macroscopic scale-invariant fluctuations emerge from the microscopic many-body excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finite-temperature behavior in a broad range of strongly correlated quantum systems.

Heavy-fermion systems share some of the strange metal phenomenology seen in other unconventional superconductors, providing a unique opportunity to set strange metals in a broader context. Central to understanding heavy-fermion systems is the interplay of localization and itinerancy. These materials acquire high electronic masses and a concomitant Fermi volume increase as the $f$ electrons delocalize at low temperatures. However, despite the wide-spread acceptance of this view, a direct microscopic verification has been lacking. Here we report high-resolution angle-resolved photoemission measurements on ${\mathrm{CeCoIn}}_5$, a prototypical heavy-fermion compound, which spectroscopically resolve the development of band hybridization and the Fermi surface expansion over a wide temperature region. Unexpectedly, the localized-to-itinerant transition occurs at surprisingly high temperatures, yet $f$ electrons are still largely localized even at the lowest temperature. These findings point to an unanticipated role played by crystal-field excitations in the strange metal behavior of ${\mathrm{CeCoIn}}_5$. Our results offer a comprehensive experimental picture of the heavy-fermion formation, setting the stage for understanding the emergent properties, including unconventional superconductivity, in this and related materials.

We present an extension of the noncrossing approximation (NCA), which is widely used to calculate properties of Anderson impurity models in the limit of infinite Coulomb repulsion $\overrightarrow{U}\infty ,$ to the case of finite U. A self-consistent conserving pseudoparticle representation is derived by symmetrizing the usual NCA diagrams with respect to empty and doubly occupied local states. This requires an infinite summation of skeleton diagrams in the generating functional thus defining the “symmetrized finite-$U$ NCA” (SUNCA). We show that within SUNCA the low-energy scale $T_K$ (Kondo temperature) is correctly obtained, in contrast to other simpler approximations discussed in the literature.