Related papers: Quantized Angular Momentum in Topological Optical …
Bulk-boundary correspondence guarantees the presence of robust, anomalous states on the boundary of topological matter. The edges of a two-dimensional Chern insulator harbor one-dimensional chiral states, which have a conductance $n\,…
The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a…
Electromagnetic topological edge states typically are created in photonic systems with crystalline symmetry and these states emerge because of the topological feature of bulk Bloch bands in momentum space according to the bulk-edge…
In this letter we show how the topological number of a static Hamiltonian can be measured from a dynamical quench process. We focus on a two-band Chern insulator in two-dimension, for instance, the Haldane model, whose dynamical process can…
A quantum quench is a nonequilibrium dynamics governed by the unitary evolution. We propose a two-band model whose quench dynamics is characterized by an arbitrary Hopf number belonging to the homotopy group $\pi _{3}(S^{2})=\mathbb{Z}$.…
The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements. Recently, it was predicted that topology can also give rise to a…
We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…
We explore theoretically how the topological properties of 2D materials can be manipulated by cavity quantum electromagnetic fields for both resonant and off-resonant electron-photon coupling, with a focus on van der Waals moir\'e…
Topological states of matter, as quantum Hall systems or topological insulators, cannot be distinguished from ordinary matter by local measurements in the bulk of the material. Instead, global measurements are required, revealing…
We report on the topological pumping of quadratic optical solitons, observed through their quantized transport in a dynamic optical potential. A distinctive feature of this system is that the two fields with different frequencies, which…
We explore the critical properties of a topological transition in a two-dimensional, amorphous lattice with randomly distributed points. The model intrinsically breaks the time-reversal symmetry without an external magnetic field, akin to a…
We provide a universal tight bound on the energy gap of topological insulators by exploring relationships between topology, quantum geometry, and optical absorption. Applications of our theory to infrared absorption near topological band…
Berry curvature that describes local geometrical properties of energy bands can elucidate many fascinating phenomena in solid-state, photonic, and phononic systems, given its connection to global topological invariants such as the Chern…
In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class…
We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where…
An interesting route to the realization of topological Chern bands in ultracold atomic gases is through the use of optical flux lattices. These models differ from the tight-binding real-space lattice models of Chern insulators that are…
A scenario of non-Hermitian bulk--boundary correspondence proposed for one-dimensional topological insulators is adapted to a non-Hermitian Chern insulator to examine its applicability to two-dimensional systems. This scenario employs bulk…
We establish the theory of critical transport in amorphous Chern insulators and show that it lies beyond the current paradigm of topological criticality epitomized by the quantum Hall transitions. We consider models of Chern insulators on…
Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that…
The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the…