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The breaking and enforcing of symmetries is a crucial ingredient in designing topologically robust materials. While magnetic fields can break time-reversal symmetry to create Chern insulators in electronic and microwave systems, at optical…
Twisted double bilayer graphene (tDBG) has emerged as an especially rich platform for studying strongly correlated and topological states of matter. The material features moir\'e bands that can be continuously deformed by both perpendicular…
We present the emergence of gapless surface states in a three-dimensional Chalker-Coddington type network model with spatial periodicity. The model consists of a ring network placed on every face of the cubic unit cells in the simple cubic…
The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields…
Three-dimensional (3D) topological materials exhibit much richer phenomena than their lower-dimensional counterparts. Here, we propose self-localized topological states (i.e., topological solitons) in a 3D nonlinear photonic Chern…
While periodically-driven phases offer a unique insight into non-equilibrium topology that is richer than its static counterpart, their experimental realization is often hindered by ubiquitous decoherence effects. Recently, we have proposed…
The concept of Chern insulators is one of the most important buliding block of topological physics, enabling the quantum Hall effect without external magnetic fields. The construction of Chern insulators has been typically through an…
A topological insulator is regarded as an ideal candidate for information storage and high-speed lossless electrical transmission devices due to robust topological protected boundary modes. Previous studies revealed that symmetry exerts an…
We study adatom-covered single layers of CrSiTe$_3$ and CrGeTe$_3$ using first-principles calculations based on hybrid functionals. We find that the insulating ground state of a monolayer of La (Lu) deposited on single-layer CrSiTe$_3$…
Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific…
We propose a novel way of modulating exceptional topology by implementing Floquet engineering in non-hermitian (NH) systems. We introduce Floquet exceptional topological insulator which results from shining light on a conventional…
The topological insulator is an electronic phase stabilized by spin-orbit coupling that supports propagating edge states and is not adiabatically connected to the ordinary insulator. In several ways it is a spin-orbit-induced analogue in…
Energy or quasienergy (QE) band spectra depending on two parameters may have a nontrivial topological characterization by Chern integers. Band spectra of 1D systems that are spanned by just one parameter, a Bloch phase, are topologically…
Chern numbers can be calculated within a frame of vortex fields related to phase conventions of a wave function. In a band protected by gaps the Chern number is equivalent to the total number of flux carrying vortices. In the presence of…
In the framework of the tight binding approximation, we study a non-interacting model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to $\Lambda$- or V-type sublattice…
The topological response to external perturbations is an effective probe to characterize different topological phases of matter. Besides the Hall conductance, the Hall viscosity is another example of such a response that measures how…
In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing…
Higher-order topological phases and real topological phases are two emerging topics in topological states of matter, which have been attracting considerable research interest. However, it remains a challenge to find realistic materials that…
Topological phases with broken time-reversal symmetry and Chern number |C|>=2 are of fundamental interest, but it remains unclear how to engineer the desired topological Hamiltonian within the paradigm of spin-orbit-coupled particles…
Symmetry plays a key role in classifying topological phases. Recent theory shows that in the presence of gauge fields, the algebraic structure of crystalline symmetries needs to be projectively represented, which enables unprecedented…