Related papers: Topological Time Crystals
We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of…
We show that time crystal phases, which are known to exist for disorder-based many-body localized systems, also appear in systems where localization is due to strong magnetic field gradients. Specifically, we study a finite Heisenberg spin…
Topological insulators are a novel class of quantum materials in which time-reversal symmetry, relativistic (spin-orbit) effects and an inverted band structure result in electronic metallic states on the surfaces of bulk crystals. These…
Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is also the proper stage to describe autonomous energy…
Hopfions, higher-dimensional topological quasiparticles with sophisticated 3D knotted spin textures discovered in condensed matter and photonic systems, show promise in high-density data storage and transfer. Here we present crystalline…
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…
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…
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of…
The spontaneous breaking of symmetries is a widespread phenomenon in physics. When time translational symmetry is spontaneously broken, an exotic nonequilibrium state of matter in which the same structures repeat themselves in time can…
Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. While discrete time crystals have been extensively studied in periodically driven systems…
We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…
Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not…
Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped…
Discrete time crystals are periodically driven systems that display spontaneous symmetry breaking of time translation invariance in the form of indefinite subharmonic oscillations. We introduce a thermodynamically consistent model for a…
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…
We demonstrate the possibility of using time-space crystalline structures to simulate eight-dimensional systems based on only two physical dimensions. A suitable choice of system parameters allows us to obtain a gapped energy spectrum,…
Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a…
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…
Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators…
Topological states of matter are robust quantum phases, characterised by propagating or localised edge states in an insulating bulk. Topological boundary states can be triggered by various mechanisms, for example by strong spin-orbit…