Related papers: Topological $\pi$ modes and beyond
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with no counterparts in topological Hermitian…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…
We extend the notion of fragile topology to periodically-driven systems. We demonstrate driving-induced fragile topology in two different models, namely, the Floquet honeycomb model and the Floquet $\pi$-flux square-lattice model. In both…
We propose a generic scattering matrix model implementable in photonics to engineer a new Floquet metallic phase that combines two distinct topological properties: the winding of the bulk bands and the existence of robust chiral edge…
Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In…
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…
A $d$-dimensional, $n$th-order topological insulator or superconductor has localized eigenmodes at its $(d-n)$-dimensional boundaries ($n\leq d$). In this work, we apply periodic driving fields to two-dimensional superconductors, and obtain…
Integrable Floquet spin chains are known to host strong zero and $\pi$ modes which are boundary operators that respectively commute and anticommute with the Floquet unitary generating stroboscopic time-evolution, in addition to…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary…
Topological phases of matter are featured with exotic edge states. However, the fractional topological numbers at edges, though predicted long ago by Jackiw and Rebbi, remain elusive in topological photonic systems. Here, we report on the…
Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on…
Stellar oscillations can be of topological origin. We reveal this deep and so-far hidden property of stars by establishing a novel parallel between stars and topological insulators. We construct an hermitian problem to derive the expression…
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…
Topological surface states, a new kind of electronic state of matter, have recently been observed on the cleaved surfaces of crystals of a handful of small band gap semiconductors. The underlying chemical factors that enable these states…
Contemporary quantum materials research is guided by themes of topology and of electronic correlations. A confluence of these two themes is engineered in "moir\'e materials", an emerging class of highly tunable, strongly correlated…
Topological insulators (TIs) are expected to be a promising platform for novel quantum phenomena, whose experimental realizations require sophisticated devices. In this Technical Review, we discuss four topics of particular interest for TI…
We derive a complete classification of Floquet phases of interacting bosons and fermions with $U(1)$ symmetry in two spatial dimensions. According to our classification, there is a one-to-one correspondence between these Floquet phases and…