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1. Migdal–Eliashberg superconductivity in a Kondo lattice

   https://doi.org/10.1088/1361-648X/ad43a5  

   Awelewa, Samuel; Dzero, Maxim (May 2024, Journal of Physics: Condensed Matter)

   We apply the Migdal–Eliashberg theory of superconductivity to heavy-fermion and mixed valence materials. Specifically, we extend the Anderson lattice model to a case when there exists a strong coupling between itinerant electrons and lattice vibrations. Using the saddle-point approximation, we derive a set of coupled nonlinear equations which describe competition between the crossover to a heavy-fermion or mixed-valence regimes and conventional superconductivity. We find that superconductivity at strong coupling emerges on par with the development of the many-body coherence in a Kondo lattice. Superconductivity is gradually suppressed with the onset of the Kondo screening and for strong electron-phonon coupling the Kondo screening exhibits a characteristic re-entrant behavior. Even though for both weak and strong coupling limits the suppression of superconductivity is weaker in the mixed-valence regime compared to the local moment one, superconducting critical temperature still remains nonzero. In the weak coupling limit the onset of the many body coherence develops gradually, in the strong coupling limit it emerges abruptly in the mixed valence regime while in the local moment regime the f-electrons remain effectively decoupled from the conduction electrons. Possibility of experimental realization of these effects in Ce-based compounds is also discussed. 

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2. Renormalizations in unconventional superconducting states of Ce1-xYbxCoIn5

   https://doi.org/DOI:10.1103/PhysRevB.99.035136  

   Ding, Z. F.; Zhang, J.; Tan, C.; Huang, K.; Lum, I.; Bernal, O. O.; Ho, P.-C.; MacLaughlin, D. E.; Maple, M. B.; Shu, L. (January 2019, Physical review. B, Condensed matter)

   We have measured the superconducting penetration depth (T ) in the heavy-fermion/intermediate-valent superconducting alloy series Ce1−xYbxCoIn5 using a transverse-field muon spin relaxation to study the effect of intermediate-valent Yb doping on Fermi-liquid renormalization. From (T ) we determine the superfluid density ρs (T ) and find that it decreases continuously with increasing nominal Yb concentration x, i.e., with increasing intermediate valence. The temperature-dependent renormalization of the “normal” fluid density ρN (T ) = ρs (0) − ρs (T ) in both the heavy-fermion and intermediate valence limits is proportional to the temperature-dependent renormalization of the specific heat. This indicates that the temperature-dependent Fermiliquid Landau parameters of the superconducting quasiparticles entering the two different physical quantities are the same. These results represent an important advance in understanding of both intermediate valence and heavy-fermion phenomena in superconductors. 

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3. Hund’s flat band in a frustrated spinel oxide

   https://doi.org/10.1073/pnas.2518213122  

   Oh, Dongjin; Hampel, Alexander; Wakefield, Joshua P; Moen, Peter C; Smit, Steef; Luo, Xiangyu; Zonno, Marta; Gorovikov, Sergey; Leandersson, Mats; Polley, Craig; et al (November 2025, Proceedings of the National Academy of Sciences)

   Electronic flat bands associated with quenched kinetic energy and heavy electron mass have attracted great interest for promoting strong electronic correlations and emergent phenomena such as high-temperature charge fractionalization and superconductivity. Intense experimental and theoretical research has been devoted to establishing the rich nontrivial metallic and heavy fermion phases intertwined with such localized electronic states. Here, we investigate the transition metal oxide spinel LiV₂O₄, an enigmatic heavy fermion compound lacking localizedforbital states. We use angle-resolved photoemission spectroscopy and dynamical mean-field theory to reveal a kind of correlation-induced flat band with suppressed interatomic electron hopping arising from intra-atomic Hund’s coupling. The appearance of heavy quasiparticles is ascribed to a proximate orbital-selective Mott state characterized by fluctuating local moments as evidenced by complementary magnetotransport measurements. The spectroscopic fingerprints of long-lived quasiparticles and their disappearance with increasing temperature further support the emergence of a high-temperature “bad” metal state observed in transport data. This work resolves a long-standing puzzle on the origin of heavy fermion behavior and unconventional transport in LiV₂O₄. Simultaneously, it opens a path to achieving flat bands through electronic interactions ind-orbital systems with geometrical frustration, potentially enabling the realization of exotic phases of matter such as the fractionalized Fermi liquids. 

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4. Flat bands, strange metals and the Kondo effect

   https://doi.org/10.1038/s41578-023-00644-z  

   Checkelsky, Joseph G; Bernevig, B Andrei; Coleman, Piers; Si, Qimiao; Paschen, Silke (February 2024, Nature Reviews Materials)

   Flat-band materials such as the kagome metals or moiré superlattices are of intense current interest. Flat bands can result from the electron motion on numerous (special) lattices and usually exhibit topological properties. Their reduced bandwidth proportionally enhances the effect of Coulomb interaction, even when the absolute magnitude of the latter is relatively small. Seemingly unrelated to these materials is the large family of strongly correlated electron systems, which include the heavy-fermion compounds, and cuprate and pnictide superconductors. In addition to itinerant electrons from large, strongly overlapping orbitals, they frequently contain electrons from more localized orbitals, which are subject to a large Coulomb interaction. The question then arises as to what commonality in the physical properties and microscopic physics, if any, exists between these two broad categories of materials. A rapidly increasing body of strikingly similar phenomena across the different platforms — from electronic localization–delocalization transitions to strange-metal behaviour and unconventional superconductivity — suggests that similar underlying principles could be at play. Indeed, it has recently been suggested that flat-band physics can be understood in terms of Kondo physics. Inversely, the concept of electronic topology from lattice symmetry, which is fundamental in flat-band systems, is enriching the field of strongly correlated electron systems, in which correlation-driven topological phases are increasingly being investigated. In this Perspective article, we elucidate this connection, survey the new opportunities for cross-fertilization across platforms and assess the prospect for new insights that may be gained into correlation physics and its intersection with electronic topology. 

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5. Symmetry-Enforced Many-Body Separability Transitions

   https://doi.org/10.1103/PRXQuantum.5.030310  

   Chen, Yu-Hsueh; Grover, Tarun (July 2024, PRX Quantum)

   We study quantum many-body mixed states with a symmetry from the perspective of , i.e., whether a mixed state can be expressed as an ensemble of short-range-entangled symmetric pure states. We provide evidence for “symmetry-enforced separability transitions” in a variety of states, where in one regime the mixed state is expressible as a convex sum of symmetric short-range-entangled pure states, while in the other regime, such a representation is not feasible. We first discuss the Gibbs state of Hamiltonians that exhibit spontaneous breaking of a discrete symmetry, and argue that the associated thermal phase transition can be thought of as a symmetry-enforced separability transition. Next we study cluster states in various dimensions subjected to local decoherence, and identify several distinct mixed-state phases and associated separability phase transitions, which also provides an alternative perspective on recently discussed “average symmetry-protected topological order.” We also study decohered $p+ip$superconductors, and find that if the decoherence breaks the fermion parity explicitly, then the resulting mixed state can be expressed as a convex sum of nonchiral states, while a fermion parity–preserving decoherence results in a phase transition at a nonzero threshold that corresponds to spontaneous breaking of fermion parity. Finally, we briefly discuss systems that satisfy the no low-energy trivial state property, such as the recently discovered good low-density parity-check codes, and argue that the Gibbs state of such systems exhibits a temperature-tuned separability transition. Published by the American Physical Society2024 

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