Related papers: Engineering Topological Phases with a Traveling-Wa…

Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. While a range of different mechanisms to induce topological order have been introduced, a quest for…

It is well known that an interface created by two topologically distinct structures could host nontrivial edge states that are immune to defects. In this letter, we introduce a one-dimensional space-time phononic crystal and study the…

Photonic time crystals are electromagnetic media with periodically time-varying parameters, enabling momentum band gaps, parametric amplification, and frequency conversion beyond what is possible in time-invariant systems. So far, they have…

Topological magnetic textures are particle-like spin configurations stabilized by competing interactions. Their formation is commonly attributed to fluctuation-driven, first-order nucleation processes requiring activation over a topological…

The effect of temporal modulation on traveling waves in the flows in two distinct systems of rotating cylinders, both with broken azimuthal symmetry, has been investigated. It is shown that by modulating the control parameter at twice the…

Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…

Spatiotemporal metasurfaces offer unique opportunities for wave manipulation, however, their practical realization is often constrained by the requirement for in-plane spatial modulation, which necessitates a large number of time-varying…

The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…

Time is the odd dimension out: Unlike space, it follows the arrow of time, forbidding back-reflections and requiring momentum yet not energy conservation. Tailored temporal variations manipulate momentum bands and engineer waves in time. We…

Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…

We introduce a novel class of interaction-enabled topological crystalline insulators in two- and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal…

While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform…

Discrete degrees of freedom, such as spin and orbital, can provide intriguing strategies to manipulate electrons, photons, and phonons. With a spin degree of freedom, topological insulators have stimulated intense interests in…

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…

We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…

Time crystals are quantum many-body systems which, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in…

Topological phases usually are unreachable in molecular solids, which are characteristic of weakly dispersed energy bands with a large gap, in contrast to topological materials. In this work, however, we propose that nontrivial electronic…

When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at…

Time-varying media, characterized by dynamic or spacetime-modulated constitutive parameters such as permittivity and permeability, have recently emerged as a transformative paradigm for advanced wave control, transcending the constraints…