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In the development of topological photonics, achieving three dimensional topological insulators is of significant interest since it enables the exploration of new topological physics with photons, and promises novel photonic devices that…
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 Chern number is a crucial topological invariant for distinguishing the phases of Chern insulators. Here we find that for Chern insulators with inversion symmetry, the Chern number alone is insufficient to fully characterize their…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
Topological insulators (TIs) are a novel class of materials with nontrivial surface or edge states. Time-reversal symmetry (TRS) protected TIs are characterized by the Z2 topological invariant and their helical property becomes lost in an…
Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on…
Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at 1/3 filling exhibits a fractional quantum Hall…
The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to…
Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here we demonstrate through numerical calculations on model wave…
We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition's first-order nature in the interacting Haldane model on the honeycomb geometry, from a mean-field…
We present an exact analytical investigation of the topological properties and edge states of the Haldane model defined on a honeycomb lattice with zigzag edges. By exploiting translational symmetry along the ribbon direction, we perform a…
Recent search for optical analogues of topological phenomena mainly focuses on mimicking the key feature of quantum Hall and quantum spin Hall effects (QHE and QSHE): edge currents protected from disorder. QHE relies on time-reversal…
Chern insulators are two-dimensional magnetic topological materials that conduct electricity along their edges via the one-dimensional chiral modes. The number of these modes is a topological invariant called the first Chern number $C$,…
In this paper, we study transport properties of non-equilibrium systems under the application of light in many-terminal measurements, using the Floquet picture. We propose and demonstrate that the quantum transport properties can be…
We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) formula. By generalizing…
Fractional Chern insulators (FCIs) in ideal flat bands with Chern number $C$ are commonly understood as color-entangled states constructed from $C$ copies of the lowest Landau level. In realistic moir\'e systems, however, the band geometry…
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 realization of Haldane's topological graphene model in practical materials has presented significant challenges. Here, we propose achieving this model by embedding graphene in chiral cavities, using the asymptotically decoupled…
In topological insulators, massive surface bands resulting from local symmetry breaking are believed to exhibit a half-quantized Hall conductance. However, such scenarios are obviously inconsistent with the Thouless-Kohmoto-Nightingale-Nijs…
Fractional quantum Hall effect (FQHE) is a prime example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order, and time reversal symmetry breaking. Recently, a lattice…