The topological phases of noninteracting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct manybody local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to nonfederal websites. Their policies may differ from this site.

Abstract U (1) particle number, they yield manybody fragile topological indices, which we use to identify which singleparticle fragile states are manybody topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with singleparticle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global manybody RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no singleparticle counterpart. Finally, we show that the manybody local RSIs appear as quantized coefficients of WenZee terms in the topological quantum field theory describing the phase.Free, publiclyaccessible full text available December 1, 2025 
Flatband 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 heavyfermion 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 strangemetal behaviour and unconventional superconductivity — suggests that similar underlying principles could be at play. Indeed, it has recently been suggested that flatband physics can be understood in terms of Kondo physics. Inversely, the concept of electronic topology from lattice symmetry, which is fundamental in flatband systems, is enriching the field of strongly correlated electron systems, in which correlationdriven topological phases are increasingly being investigated. In this Perspective article, we elucidate this connection, survey the new opportunities for crossfertilization across platforms and assess the prospect for new insights that may be gained into correlation physics and its intersection with electronic topology.more » « lessFree, publiclyaccessible full text available February 20, 2025

Free, publiclyaccessible full text available December 1, 2024

Abstract Geometrically frustrated kagome lattices are raising as novel platforms to engineer correlated topological electron flat bands that are prominent to electronic instabilities. Here, we demonstrate a phonon softening at the
k _{z} =π plane in ScV_{6}Sn_{6}. The low energy longitudinal phonon collapses at ~98 K andq = due to the electronphonon interaction, without the emergence of longrange charge order which sets in at a different propagation vector$$\frac{1}{3}\frac{1}{3}\frac{1}{2}$$ $\frac{1}{3}\frac{1}{3}\frac{1}{2}$q _{CDW} = . Theoretical calculations corroborate the experimental finding to indicate that the leading instability is located at$$\frac{1}{3}\frac{1}{3}\frac{1}{3}$$ $\frac{1}{3}\frac{1}{3}\frac{1}{3}$ of a rather flat mode. We relate the phonon renormalization to the orbitalresolved susceptibility of the trigonal Sn atoms and explain the approximately flat phonon dispersion. Our data report the first example of the collapse of a kagome bosonic mode and promote the 166 compounds of kagomes as primary candidates to explore correlated flat phonontopological flat electron physics.$$\frac{1}{3}\frac{1}{3}\frac{1}{2}$$ $\frac{1}{3}\frac{1}{3}\frac{1}{2}$Free, publiclyaccessible full text available December 1, 2024 
Electronic structure calculations indicate that the Sr_{2}FeSbO_{6}double perovskite has a flatband set just above the Fermi level that includes contributions from ordinary subbands with weak kinetic electron hopping plus a flat subband that can be attributed to the lattice geometry and orbital interference. To place the Fermi energy in that flat band, electrondoped samples with formulas Sr_{2}
_{x} La_{x} FeSbO_{6}(0 ≤x ≤ 0.3) were synthesized, and their magnetism and ambient temperature crystal structures were determined by highresolution synchrotron Xray powder diffraction. All materials appear to display an antiferromagneticlike maximum in the magnetic susceptibility, but the dominant spin coupling evolves from antiferromagnetic to ferromagnetic on electron doping. Which of the three subbands or combinations is responsible for the behavior has not been determined.