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A band with a nonzero Chern number cannot be fully localized by weak disorder. There must remain at least one extended state, which ``carries the Chern number.'' Here we show that a trivial band can behave in a similar way. Instead of fully…
For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity.…
A central property of Chern insulators is the robustness of the topological phase and edge states to impurities in the system. Despite this, Chern number cannot be straightforwardly calculated in the presence of disorder. Recently, work has…
This paper demonstrates the existence of topological models with gapped edge states but protected extended bulk states against disorder. Such systems will be labeled as trivial by the current classification of topological insulators. Our…
It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize when the bulk correlation length diverges.…
We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with…
Topological insulators are characterized by specially protected conduction on their outer boundaries. We show that the protected edge conduction exhibited by 2-D topological insulators (and also Chern insulators) is independent of…
Nodal superconductors without inversion symmetry exhibit nontrivial topological properties, manifested by topologically protected flat-band edge states. Here we study the effects of breaking translational symmetry, crucial to the definition…
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…
Quantum Hall systems host chiral edge states extending along the one-dimensional boundary of any two-dimensional sample. In solid state materials, the edge states serve as perfectly robust transport channels that produce a quantised Hall…
Robustness against disorder and defects is a pivotal advantage of topological systems, manifested by absence of electronic backscattering in the quantum Hall and spin-Hall effects, and unidirectional waveguiding in their classical analogs.…
We analyse the topological transition and localization evolution of disordered two dimensional systems with non trivial topology based on bipartite lattices. Chern insulators with broken time reversal symmetry show non standard behavior for…
Conventional Chern insulators are two-dimensional periodic structures that support unidirectional edge states at the boundary, while the wave propagation in the bulk regions is forbidden. The number of unidirectional edge states is governed…
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…
Here we study the instabilities of a quadratic band crossing system to Chern insulating states and uncorrelated disorder. We determined the phase diagram in the plane of topological mass versus disorder strength, characterizing the system…
We examine the role of strong nonlinearity on the topologically-robust edge state in a one-dimensional system. We consider a chain inspired from the Su-Schrieffer-Heeger model, but with a finite-frequency edge state and the dynamics…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
We study the effect of strong disorder on topology and entanglement in quench dynamics. Although disorder-induced topological phases have been well studied in equilibrium, the disorder-induced topology in quench dynamics has not been…
Spin chains with symmetry-protected edge zero modes can be seen as prototypical systems for exploring topological signatures in quantum systems. These are useful for robustly encoding quantum information. However in an experimental…
The non-Hermitian skin effect can arise in materials that have asymmetric hoppings between atoms or resonating units, which makes the bulk eigenspectrum sensitive to boundary conditions. When skin effect emerges, eigenstates in the bulk…