相关论文: Measuring quantized circular dichroism in ultracol…
Topological properties of energy spectra of general one-dimensional quasiperiodic systems, describing also Bloch electrons in magnetic fields, are studied for an infinity of irrational modulation frequencies corresponding to irrational…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
We propose a simple scheme for the realization of a topological quasienergy band structure with ultracold atoms in a periodically driven optical square lattice. It is based on a circular lattice shaking in the presence of a superlattice…
The manipulation of particle transport in synthetic quantum matter is an active research frontier for its theoretical importance and potential applications. Here we experimentally demonstrate an engineered topological transport in a…
We investigate relations between topology and the quantum metric of two-dimensional Chern insulators. The quantum metric is the Riemannian metric defined on a parameter space induced from quantum states. Similar to the Berry curvature, the…
We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the 2+1 dimensional momentum algebra, which includes a central extension proportional to the…
We study the polaritonic bandstructure of two-dimensional atomic lattices coupled to a single excitation of a surface plasmon polariton mode. We show the possibility of realizing topological gaps with different Chern numbers by having…
A peculiar feature of the majority of three dimensional topological insulator surface states studied experimentally thus far, namely their particle-hole asymmetry, makes quantum oscillations (Shubnikov de Haas and de Haas van Alphen…
We rigorously yet concisely prove the bulk-edge correspondence for general $d$-dimensional ($d$D) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index.…
Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a…
The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…
A set of recent results indicates that fractionally filled bands of Chern insulators in two dimensions support fractional quantum Hall states analogous to those found in fractionally filled Landau levels. We provide an understanding of…
The quantum geometry of Bloch wavefunctions,encoded in the Berry curvature and quantum metric, is believed to be a decisive ingredient in stabilizing fractional quantum anomalous Hall (FQAH) effect(i.e., fractional Chern insulator, FCI, at…
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…
Few level quantum systems driven by $n_\mathrm{f}$ incommensurate fundamental frequencies exhibit temporal analogues of non-interacting phenomena in $n_\mathrm{f}$ spatial dimensions, a consequence of the generalisation of Floquet theory in…
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…
When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of {\em…
The Chern topological numbers of a material system are traditionally written in terms of the Berry curvature which depends explicitly on the material band structure and on the Bloch eigenwaves. Here, we demonstrate that it is possible to…
Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of…
It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems -- fractional Chern insulators and the fractional…