Related papers: Flat bands with higher Chern number in pyrochlore …
Bi-layer Kagome compounds provide an exciting playground where the interplay of topology and strong correlations can give rise to exotic phases of matter. Motivated by recent first principles calculation on such systems (Phys. Rev. Lett…
We address the question of whether fractionally filled bands with a nontrivial Chern index in zero external field could also exhibit a Fractional Quantum Hall Effect (FQHE). Numerical works suggest this is possible. Analytic treatments are…
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…
Topological properties of a certain class of spinless three-band Hamiltonians are shown to be summed up by the Skyrmion number in momentum space, analogous to the case of two-band Hamiltonian. Topological tight-binding Hamiltonian on a…
Recent developments in fractional quantum Hall (FQH) physics highlight the importance of studying FQH phases of particles partially occupying energy bands that are not Landau levels. FQH phases in the regime of strong lattice effects,…
The classification of bandstructures by topological invariants provides a powerful tool for understanding phenomena such as the quantum Hall effect. This classification was originally developed in the context of electrons, but can also be…
We theoretically investigate a photonic Kagome lattice which can be realized in microwave cavity arrays using current technology. The Kagome lattice exhibits an exotic band structure with three bands one of which can be made completely…
A Chern band is characterized by a Wannier obstruction indicating the absence of a basis of complete, orthogonal, and exponentially-localized states. Here, we study the properties of real space bases of a Chern band obtained by relaxing…
We use the tensor network algorithm to show evidences of a non-uniform chiral spin-liquid (CSL) ground state in a frustrated spin-1/2 model on a square lattice, in the regime of moat-like band structure of the lattice, i.e., a band with…
Many graphene moir\'e superlattices host narrow bands with non-zero valley Chern numbers. We provide analytical and numerical evidence for a robust spin and/or valley polarized insulator at total integer band filling in nearly flat bands of…
The realization of fractional Chern insulators in moir\'e materials has sparked the search for further novel phases of matter in this platform. In particular, recent works have demonstrated the possibility of realizing quantum anomalous…
The interplay between strong electron-electron interaction and symmetry breaking can have profound influence on the topological properties of materials. In magic angle twisted bilayer graphene (MATBG), the flat band with a single SU(4)…
We study fractional quantum Hall states with quasihole excitations, on Riemann surfaces of arbitrary genus. For configurations with $m$ quasiholes we construct a vector bundle above the $m$-th symmetric power of the curve so that the fiber…
Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum phase transitions triggered by enhanced electron-electron interactions when its flat-bands are partially filled. However, the phases themselves and their connection…
Enhancing the many-body gap of a fractional state is crucial for realizing robust fractional excitations. For fractional Chern insulators, existing studies suggest that making flat Chern bands closely resemble the lowest Landau level (LLL)…
We report the discovery of flatten Bloch bands with nontrivial topological numbers in a quasi-one-dimensional sawtooth chain. We present the nearly flat-band with a obvious gap and nonzero Chern number of the modulated sawtooth chain by…
We predict the van der Waals monolayer ReAg$_2$Cl$_6$ hosts isolated flat Chern bands at the Fermi level in its $120^\circ$ antiferromagnetic ground state. Their flatness and nontrivial topology arise from the cooperative effect of coplanar…
Haldane's tight-binding model, which describes a Chern insulator in a two-dimensional hexagonal lattice, exhibits quantum Hall conductivity without an external magnetic field. Here, we explore an $\alpha -T_{3}$ lattice subjected to…
Flat band systems are usually associated to compact localized states (CLSs) resulting from the macroscopic degeneracy of eigenstates at the flat band energy. In case of singular flat bands, these conventional localized flat band states have…
We consider a hitherto unexplored setting of stacked multilayer ($\mathcal{N}$) Lieb lattice which undergoes an unusual topological transition in the presence of intra-layer spin-orbit coupling (SOC). The specific stacking configuration…