相关论文: Topological BF description of 2D accelerated chira…

We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern…

Quantum Hall edge modes are chiral while quantum spin Hall edge modes are helical. However, unlike chiral edge modes which always occur in topological systems, quasi-helical edge modes may arise in a trivial insulator too. These trivial…

A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the "wrong" chirality. This leads to pairs of counter-propagating chiral edge modes at each edge,…

It is now well-established that photonic systems can exhibit topological energy bands; similar to their electronic counterparts, this leads to the formation of chiral edge modes which can be used to transmit light in a manner that is…

One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial…

In this paper the 3D Maxwell theory with single-sided planar boundary is studied. As a consequence of the existence, on the boundary, of two Ward identities, we find two chiral conserved edge currents satisfying a Ka\c{c}-Moody algebra with…

Time periodic driving serves not only as a convenient way to engineer effective Hamiltonians, but also as a means to produce intrinsically dynamical phases that do not exist in the static limit. A recent example of the latter are 2D chiral…

An alternative approach to introducing gravitational dynamics on a brane embedded in a higher dimensional spacetime is presented. The brane is treated as a boundary of a higher dimensional manifold in which the bulk action is described by a…

Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…

Unlike the edge state of a topological insulator where its energy level lives in the bulk energy gap, the edge state of a topological semimetal hides in the bulk spectrum and is difficult to be identified by the energy. We investigate the…

We propose the concept of 2D non-Abelian topological insulator which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we…

We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological…

We study the topological properties of one-dimensional discrete-time quantum walks with Fibonacci quasiperiodic modulation. Spectral analysis under open boundary conditions reveals isolated edge modes that coexist at both zero and $\pi$…

Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While…

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the…

We present a field theoretical analysis of the 2+1 dimensional BF model with boundary in the Abelian and the non-Abelian case based on the Symanzik's separability condition. In both cases on the edges we obtain Ka\v{c}--Moody algebras with…

Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner…

According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines topological order in the gapped bulk. As the bulk is less accessible, the last two decades saw the emergence of…

Many examples from quantum and classical physics are known where topological protection is responsible for the robustness of the dynamics. Less explored is the role of topological protection in the context of classical oscillatory systems.…

Edge states reveal the nontrivial topology of energy band in the bulk. As localized states at boundaries, many-body edge states may obey a special symmetry that is broken in the bulk. When local particle-particle interaction is induced,…