[Paper Review] Flat bands, strange metals, and the Kondo effect

J. G. Checkelsky, B. Andrei Bernevig+3 more|arXiv (Cornell University)|Dec 17, 2023

Iron-based superconductors research193 references4 citations

TL;DR

This paper proposes a unifying framework linking flat band systems and strongly correlated electron systems through Kondo physics and electronic topology. It demonstrates that flat bands—especially topological ones—can be understood as emergent Kondo phenomena, while Kondo physics enriches topological quantum matter, revealing shared mechanisms in strange metallicity and unconventional superconductivity.

ABSTRACT

Flat band materials such as the kagome metals or moiré superlattice systems 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 cases is the large family of strongly correlated electron systems, which includes the heavy fermion compounds, 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 the 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 behavior 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 where correlation-driven topological phases are increasingly being investigated. Here we elucidate this connection, survey the new opportunities for cross-fertilization in understanding across the platforms, and assess the prospect for new insights that may be gained into both the correlation physics and its intersection with electronic topology.

Motivation & Objective

• To identify common physical principles underlying flat band materials and strongly correlated electron systems, despite their differing electronic origins.
• To investigate the role of Kondo physics in mediating localization-delocalization transitions and strange metal behavior in flat band systems.
• To explore how electronic topology—arising from lattice symmetry—can stabilize and enrich correlation-driven topological phases.
• To assess the potential for cross-fertilization between moiré superlattices, kagome metals, and Kondo insulators in discovering new quantum phases.
• To examine whether topological superconductivity and fractional Chern insulators can emerge from Kondo-driven flat bands.

Proposed method

• Analyzing the interplay between electron correlations (U) and bandwidth (W) in flat band systems, particularly through the U/W ratio as a control parameter.
• Applying Kondo model frameworks to describe localized electrons coupled to conduction bands in topological flat band materials.
• Using topological invariants and symmetry constraints (e.g., space group symmetries) to classify and predict novel topological phases in correlated systems.
• Surveying experimental signatures across platforms—such as quantum oscillations, resistivity scaling, and edge states—to identify universal behavior.
• Leveraging Green’s function techniques and non-perturbative methods to treat strong correlations and topology simultaneously.
• Drawing analogies between Kondo-driven Weyl nodes and topological flat bands to unify descriptions of quantum criticality and strange metallicity.

Experimental results

Research questions

• RQ1 Can flat band physics be understood as an emergent form of Kondo physics, particularly in systems with topological band structures?
• RQ2 To what extent do Kondo effects and topological order coexist and mutually stabilize in strongly correlated materials like kagome metals and moiré systems?
• RQ3 What is the role of quantum criticality and entanglement in linking strange metal behavior to topological superconductivity?
• RQ4 Can fractional Chern insulating states be realized in Kondo insulators through strong correlations and topology?
• RQ5 How do symmetry-enriched Kondo models—incorporating topology and strong correlations—predict new phases of matter?

Key findings

• Flat band systems, particularly those with topological character such as kagome metals and moiré superlattices, exhibit enhanced correlation effects due to vanishing bandwidth, mimicking strong Kondo coupling.
• Strange metal behavior in flat bands arises when effective band flatness diverges, signaling a localization-delocalization transition akin to Kondo quantum criticality.
• Topological flat bands in materials like CoSn and magic-angle twisted bilayer graphene (MATBG) host signatures of fractional Chern insulators, suggesting a deep link to Kondo-driven topological order.
• Kondo physics in systems like Ce3Bi4Pd3 stabilizes Weyl nodes and supports topological semimetal phases, indicating that Kondo screening can generate topological protection.
• The emergence of topological superconductivity in flat bands is strongly linked to Kondo-driven quantum criticality, with evidence from resistivity scaling and non-Fermi liquid behavior.
• Maximal many-body entanglement at Kondo destruction quantum critical points—characteristic of strange metals—suggests a shared origin with topological quantum phases, including quantum spin liquids.