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Periodically driven systems host topological phases without static analogs, such as the anomalous Floquet phase characterized by trivial bulk bands yet robust boundary modes. In this work, we investigate the scattering problem of a Floquet…

We present an effective field theory approach to the topological response of Floquet systems with symmetry group $G$. This is achieved by introducing a background $G$ gauge field in the Schwinger-Keldysh formalism, which is suitable for far…

We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the $\nu=1/2$ fractional quantum Hall effect on the lattice. We address the…

The warping effect on the fractional quantum Hall (FQH) states in topological insulators is studied theoretically. Based on the perturbed wavefunctions, which include contributions from the warping term, analytical expressions for Haldane's…

We give field theory descriptions of the time-reversal invariant quantum spin Hall insulator in 2+1 dimensions and the particle-hole symmetric insulator in 1+1 dimensions in terms of massive Dirac fermions. Integrating out the massive…

Non-Abelian (NA) fractional topological states with quasi-particles obeying NA braiding statistics have attracted intensive attentions for both its fundamental nature and the prospect for topological quantum computation. To date, there are…

While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac spectrum at their boundary, it remains elusive to develop a {\it hydrodynamic} or…

We study two species of (or spin-1/2) fermions with short-range intra-species repulsion in the presence of opposite (effective) magnetic field, each at Landau level filling factor 1/3. In the absence of inter-species interaction, the ground…

A flat band with Chern number $C=0$, and well isolated from the rest of Hilbert space by a gap much larger than interaction strength, is a context that has not been regarded as relevant for fractional quantum Hall physics. In this work, we…

Rhombohedral stacked multilayer graphene is an ideal platform to search for correlated electron phenomena, due to its pair of flat bands touching at zero energy and further tunability by an electric field. Furthermore, its valley-dependent…

We propose searching for Chern insulators by depositing atomic layers of elements with large spin-orbit coupling (e.g., Bi) on the surface of a magnetic insulator. We argue that such systems will typically have isolated surface bands with…

We experimentally realized Floquet topological photonic insulators using a square lattice of direct-coupled octagonal resonators. Unlike previously reported topological insulator systems based on microring lattices, the nontrivial…

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be…

Fractional Chern insulators are lattice analogs of fractional quantum Hall states that realize fractionalized quasiparticles without an external magnetic field. A key strategy to understand and design these phases is to map Chern bands onto…

Recent advances in optics and time-resolved techniques have facilitated the exploration of new states of matter under nonequilibrium conditions. Here, we predict that irradiated graphene can host two novel nonequilibrium steady states of…

We theoretically study the real-time dynamics of the photoinduced topological phase transition to a nonequilibrium Floquet Chern insulator in an organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$, which was recently predicted using the Floquet…

We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional…

Based on the symmetry properties of graphene lattice, we derive the effective Hamiltonian of graphene under spatially non-uniform acoustic and optical strains. We show that with the proper selection of the parameters, the obtained…

We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin-1/2 particles carrying out a discrete-time quantum walk in a two-dimensional lattice. By Floquet engineering the quantum-walk protocol, an…

We analyze, in exact terms, multiband 2D itinerant correlated fermionic systems with many-body spin-orbit interactions, and in-plane external magnetic fields. Even if such systems with broad applicability in leading technologies are…