Related papers: Higher-order Topological Hyperbolic Lattices
Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a…
Understanding crystal growth and morphology is a fundamental issue in condensed matter physics. While crystal morphology due to the distribution and dynamics of the diffusion field has been intensively studied, how the intrinsic material…
Two-dimensional ferromagnetic N-state clock models are studied on a hyperbolic lattice represented by tessellation of pentagons. The lattice lies on the hyperbolic plane with a constant negative scalar curvature. We observe the spontaneous…
Photonic modes exhibiting a polarization winding akin to a vortex possess an integer topological charge. Lasing with topological charge 1 or 2 can be realized in periodic lattices of up to six-fold rotational symmetry. Higher order charges…
Topological phases have been extensively studied primarily in crystalline systems with translational symmetry. Recent theoretical studies, however, have demonstrated the existence of topological phases in quasicrystals that are absent in…
In this work, we consider 2D $\mathbb{Z}_2$ topologically ordered phases ($\mathbb{Z}_2$ toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a…
Topological photonics provides a new degree of freedom to robustly control electromagnetic fields. To date, most of established topological states in photonics have been employed in Euclidean space. Motivated by unique properties of…
Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order…
Rapid development of topological concepts in photonics unveils exotic phenomena such as unidirectional propagation of electromagnetic waves resilient to backscattering at sharp bends and disorder-immune localization of light at stable…
Higher order topological insulators are a new class of topological insulators in dimensions $\rm d>1$. These higher-order topological insulators possess $\rm (d - 1)$-dimensional boundaries that, unlike those of conventional topological…
The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been…
We show that one-dimensional quasi-periodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on…
Higher-order topological superfluids have gapped bulk and symmetry-protected Majorana zero modes with various localizations. Motivated by recent advances, we present a proposal for synthesizing multi-order topological superfluids that…
In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected…
We propose a minimal interacting lattice model for two-dimensional class-$D$ higher-order topological superconductors with no free-fermion counterpart. A Lieb-Schultz-Mattis-type constraint is proposed and applied to guide our lattice model…
Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are…
Hyperbolic lattices are starting to be explored in search of novel phases of matter. At the same time, non-Hermitian physics has come to the forefront in photonic, optical, phononic, and condensed matter systems. In this work, we introduce…
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…
In two dimensions, Hermitian lattices with non-zero Chern numbers and non-Hermitian lattices with a higher-order skin effect (HOSE) bypass the constraints of the Nielsen-Ninomiya no-go theorem at their one-dimensional boundaries. This…
High-order topological phases of matter refer to the systems of $n$-dimensional bulk with the topology of $m$-th order, exhibiting $(n-m)$-dimensional boundary modes and can be characterized by topological pumping. Here, we experimentally…