Related papers: Ideal topological flat bands in chiral symmetric m…
We present the appearance of nearly flat band states with nonzero Chern numbers in a two-dimensional "diamond-octagon" lattice model comprising two kinds of elementary plaquette geometries, diamond and octagon, respectively. We show that…
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…
Topological flat bands at the Fermi level offer a promising platform to study a variety of intriguing correlated phase of matter. Here we present band engineering in the twisted orbital-active bilayers with spin-orbit coupling. The symmetry…
We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a…
Dispersionless bands, such as Landau levels, serve as a good starting point for obtaining interesting correlated states when interactions are added. With this motivation in mind, we study a variety of dispersionless ("flat") band structures…
Narrow band electron systems are particularly likely to exhibit correlated many-body phases driven by interaction effects. Examples include magnetic materials, heavy fermion systems, and topological phases such as fractional quantum Hall…
Twisted moir\'e superlattices hosting topological flat bands provide a platform to explore the interplay between topology and correlations. Here we investigate topological band structures in $\Gamma$-valley moir\'e systems based on…
Motivated by the recent theoretical studies on a two-dimensional (2D) chiral Hamiltonian based on the Su-Schrieffer-Heeger chains, we experimentally and computationally demonstrate that topological flat frequency bands can occur at open…
We present a theoretical study of mapping between Chern bands and generalized Landau levels in twisted bilayer MoTe$_2$ ($t$MoTe$_2$), where fractional Chern insulators down to zero magnetic fields have been observed. We construct an exact…
Flat band (FB) systems provide ideal playgrounds for studying correlation physics, whereas multi-orbital characteristics in real materials are distinguished from most simple FB models. Here, we propose a systematic and versatile framework…
Quantum geometry is universally bounded from below by Wilson-loop windings. In this work, we define an isolated set of bands to be Wilson-loop-ideal, if their quantum metric saturates the Wilson-loop lower bound. The definition naturally…
The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material…
Fractional quantum anomalous Hall (FQAH) effect, a lattice analogue of fractional quantum Hall effect, offers a unique pathway toward fault-tolerant quantum computation and deep insights into the interplay of topology and strong…
We study flat bands and their topology in 2D materials with quadratic band crossing points (QBCPs) under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for QBCPs serves as a…
In this article, a new and natural topology on the prime spectrum is established which behaves completely as the dual of the Zariski topology. It is called the flat topology. The basic and also some sophisticated properties of the flat…
Certain lattices with specific geometries have one or more spectral bands that are strictly flat, i.e. the electron energy is independent of the momentum. This can occur robustly irrespective of the specific couplings between the lattices…
The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical…
We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary…
Strong interactions in Landau flat bands are known to stabilize correlated states that do not form in other types of flat bands. We report hallmarks of topological protection at the Landau level filling factor v=7/11 in a two-dimensional…
We introduce the concept of "quantum geometric nesting'' (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence…