Related papers: Topological $\pi$ modes and beyond
Time-periodic (Floquet) topological phases of matter exhibit bulk-edge relationships that are more complex than static topological insulators and superconductors. Finding the edge modes unique to driven systems usually requires numerics.…
We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…
Anomalous Floquet topological phases are a hallmark, without a static analog, of periodically driven systems. Recently, Quantum Floquet Engineering has emerged as an interesting approach to cavity-QED materials, which recovers the physics…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
Higher-order topological materials with topologically protected states at the boundaries of their boundaries (hinges or corners) have attracted attention in recent years. In this paper, we utilize time-periodic driving to generate…
In this perspective, we discuss the unique electronic properties of helical liquids appearing at the boundaries of time-reversal-invariant topological materials and highlight the key challenges impeding progress in this field. We advocate…
We present universal characteristics of quantum entanglement and topology through virtual entanglement modes that fluctuate into existence in subsystem measurements. For generic interacting systems and extensive conserved quantities, these…
Topological phonon modes are robust vibrations localized at the edges of special structures. Their existence is determined by the bulk properties of the structures and, as such, the topological phonon modes are stable to changes occurring…
For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems…
Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
We theoretically examine the use of a statistical distance measure, the indistinguishability, as a generic tool for the identification of topological order. We apply this measure to the toric code and two fractional quantum Hall models. We…
We extend topological string methods in order to perform WKB approximations for quantum mechanical problems with higher order potentials efficiently. This requires techniques for the evaluation of the relevant quantum periods for Riemann…
Topological phase, a novel and fundamental role in matter, displays an extraordinary robustness to smooth changes in material parameters or disorder. A crossover between topological physics and quantum information may lead to inherent…
Discrete Floquet time crystals (DFTC) are characterized by the spontaneous breaking of the discrete time-translational invariance characteristic of Floquet driven systems. In analogy with equilibrium critical points, also time-crystalline…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time…
Geometrical and topological phases play a fundamental role in quantum theory. Geometric phases have been proposed as a tool for implementing unitary gates for quantum computation. A fractional topological phase has been recently discovered…
The introduction of synthetic dimensions in topological photonic systems enriches the exploration of topological phase of light in higher-dimensional space beyond three-dimensional real-space. Recently, the gapless corner modes of…
Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a…