Ordered Electron Interactions Reveal a New State of Matter

Scientists have, for the first time, directly observed an ordered wave of Kondo hybridization in the heavy-fermion superconductor UTe2. Xin Yu and Shuikang Yu, from the Cavendish Laboratory, University of Cambridge, led the research, working with colleagues including Zheyu Wu, Alexander G. Eaton, Andrej Cabala from the Institute of Physics of the Czech Academy of Sciences, Michal Vališka, Jun Li, Rui Zhou, Yi-feng Yang, Zhenyu Wang, Peijie Sun and Rui Wu. This breakthrough, achieved using scanning tunneling microscopy, reveals a spatially modulated pattern, a Kondo hybridization wave, manifesting as a periodically arranged Fano lattice alongside a charge density wave. The observation is significant because it challenges the conventional understanding of Kondo hybridization as a gradual process and offers potential insights into the unusual spin-triplet pairing symmetry and superconductivity mechanism within UTe2, potentially reshaping our understanding of strongly correlated electron systems.

Until now, Kondo hybridization, the interaction between localized electrons and conducting electrons, has been understood as a gradual process, lacking a clearly defined ordered state. Now, for the first time, scientists have observed an ordered Kondo hybridization wave (KHW) on the surface of the heavy-fermion superconductor UTe2 using scanning tunneling microscopy. This KHW is accompanied by a commensurate charge density wave, meaning its charge distribution has a specific, measurable periodicity, and a pronounced energy gap, creating a unique Kondo superlattice.

Scientists have, for the first time, directly observed an ordered wave-like pattern arising from the interaction between localized and conducting electrons within the material UTe2. This discovery challenges previous understandings of this interaction as a gradual process. Instead, it reveals a distinct, organized state. The finding potentially unlocks new insights into complex materials exhibiting unconventional superconductivity, a phenomenon where electricity flows with no resistance. Scientists have, for the first time, directly observed an ordered wave-like pattern stemming from the interaction between localized and conducting electrons within the material UTe2. Understanding this interaction, known as Kondo hybridization, is crucial because it underpins many exotic quantum states in materials; imagine a group of musicians where some play fixed chords (localized electrons) and others improvise (itinerant electrons), and hybridization is how their sounds blend.

This newly observed pattern, a Kondo hybridization wave, appears alongside a commensurate charge density wave, which is like soldiers marching in perfect, evenly spaced rows, indicating a highly organized arrangement of electrical charge. The discovery challenges existing theories that previously described Kondo hybridization as a gradual process, suggesting a more defined, ordered state is possible. This finding utilizes scanning tunneling microscopy, a technique akin to mapping a surface with an incredibly fine fingertip using electrons instead of touch, to reveal atomic-level details.

Ordered Kondo Hybridization and Fano Lattice Formation in UTe2

Naren Manjunath from the Perimeter Institute and colleagues previously relied on broad crossovers to characterise Kondo hybridization. Now, scanning tunneling microscopy reveals a distinct, ordered Kondo hybridization wave in UTe2, a heavy-fermion superconductor, signifying a threshold where hybridization transitions from gradual to ordered. This unprecedented observation manifests as a periodically modulated Fano lattice, a specific interference pattern in electron tunneling, accompanied by a commensurate charge density wave, meaning its charge distribution exhibits measurable periodicity.

The resulting Kondo superlattice features a unique arrangement of heavy f-electrons and conduction electrons, coexisting with superconductivity and potentially clarifying the material’s unusual spin-triplet pairing. Real-space modulations beyond the crystal lattice were revealed in the Fano parameters, confirmed by fast Fourier transforms showing peaks at specific wavevectors, indicating the emergence of the hybridization wave. The ordered hybridization displays a unique spatial distribution of heavy f-electrons and conduction electrons, coexisting with superconductivity, while theoretical calculations confirm the nonequivalent coupling of uranium f-orbitals with tellurium p-orbitals. These findings have implications for the development of more accurate theoretical models for strongly correlated electron systems, materials where electron interactions dominate, and could provide insights into the material’s bulk properties.

Atomic Resolution Imaging of UTe2 Surface Electronic Structure

Scanning tunneling microscopy proved key in revealing the ordered Kondo hybridization wave observed in UTe2, functioning much like mapping a surface with an incredibly fine fingertip to discern its hills and valleys. This technique uses electrons to achieve atomic-level resolution of the material’s surface, rather than relying on physical touch. By carefully controlling the distance between a sharp metallic tip and the sample, electrons can ‘tunnel’ across the gap, creating a current sensitive to the surface’s electronic structure, and variations in this current then build up an image.

UTe2 samples, measuring several millimetres in size, were investigated using scanning tunneling microscopy at temperatures down to 1.4 Kelvin. The technique was favoured over bulk-sensitive probes because it directly maps the electronic structure with atomic resolution. Precise control of the metallic tip allowed observation of Kondo hybridization and the emergence of a charge density wave, a periodic arrangement of electrical charge.

Ordered Kondo hybridisation observed at the surface of the heavy-fermion superconductor UTe2

Kondo lattices are typically viewed as systems undergoing gradual transitions, but this research demonstrates a surprisingly ordered state of hybridization within the heavy-fermion superconductor UTe2. These observations, however, are currently confined to the material’s surface, leaving open the vital question of whether this ordered hybridization extends into the bulk, or remains a purely surface phenomenon. Establishing this depth is important, as a surface effect would sharply limit the implications for understanding the material’s overall behaviour and its potential for applications. The discovery of an ordered Kondo hybridization wave in UTe2 fundamentally alters the understanding of how localized and conducting electrons interact.

The blending of electron behaviour, previously considered a gradual process, now demonstrably exhibits an organised, wave-like state on the material’s surface. This ordered state, revealed through scanning tunneling microscopy, manifests as a Fano lattice, a specific interference pattern. This finding represents a strong step forward in understanding strongly correlated materials and establishes a new benchmark for theoretical models attempting to describe them.

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