Related papers: The theory of topological-topological flat bands
Topological flat bands (FBs) offer an ideal platform for realizing exotic topological phases, such as fractional Chern insulators, yet their realization with both exact flatness and stable topology in local lattice models has been long…
Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…
We report the theoretical discovery of a large class of 2D tight-binding models containing nearly-flat bands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of…
We review recent progresses in the study of flat band systems, especially focusing on the fundamental physics related to the singularity of the flat band's Bloch wave functions. We first explain that the flat bands can be classified into…
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…
We study ``frustrated'' hopping models, in which at least one energy band, at the maximum or minimum of the spectrum, is dispersionless. The states of the flat band(s) can be represented in a basis which is fully localized, having support…
Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this…
Flat bands can be divided into singular and non-singular ones according to the behavior of their Bloch wave function around band-crossing points in momentum space. We analyze the flat band in the Dice model, which can be tuned by a uniaxial…
Flat bands and dispersive Dirac bands are known to coexist in the electronic bands in a two-dimensional kagome lattice. Including the relativistic spin-orbit coupling, such systems often exhibit nontrivial band topology, allowing for…
Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strong correlation phenomena. In certain lattices with built-in geometrical frustration, electronic…
Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and in classical electric-circuit networks, we study flat bands and band-touching phenomena in such lattices. We analyze…
Nodal noncentrosymmetric superconductors have topologically nontrivial properties manifested by protected zero-energy surface states. Specifically, it was recently found that zero-energy surface flat bands of topological origin appear at…
We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits…
Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to…
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…
Motivated by the abundance of symmetry breaking states in magic-angle twisted bilayer graphene and other two-dimensional materials, we study superconducting (SC) and charge orders in two-dimensional topological flat bands in the strong…
We introduce a non-Abelian kagome lattice model that has both time-reversal and inversion symmetries and study the flat band physics and topological phases of this model. Due to the coexistence of both time-reversal and inversion…
Flat-band topologies and localizations in non-interacting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in…
We report the appearance of multiple numbers of completely flat band states in an extended Lieb lattice model in two dimensions with five atomic sites per unit cell. We also show that this edge-centered square lattice can host intriguing…
Noncontractible loop states (NLSs) are recently realized topological entity in flatband lattices, arising typically from band touching at a point where a flat band intersects one or more dispersive bands. There exists also band touching…