Related papers: Universal Continuum Theory for Topological Edge So…
We develop a formalism to extend, simultaneously, the usual definition of bulk and edge indices from topological insulators to the case of a finite sample with open boundary conditions, and provide a physical interpretation of these…
We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the…
The time evolution of topological systems is an active area of interest due to their expected applications in fault-tolerant quantum computing. Here, we analyze the dynamics of a noninteracting spinless fermion chain in its topological…
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…
The Toda lattice is a model of nonlinear wave equations allowing exact soliton solutions. It is realized by an electric circuit made of a transmission line with variable capacitance diodes and inductors. It has been generalized to the…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…
We study the properties of one-dimensional topological superconductors under the influence of generic boundary conditions mimicking the coupling with external environments. We identify a general four-parameters classification of the…
Topological phononic crystals have attracted intensive attention due to their peculiar topologically protected interface or edge states. Their operating frequency, however, is generally fixed once designed and fabricated. Here, we propose…
We develop a theory of bound states in the continuum (BICs) in multipolar lattices -- periodic arrays of resonant multipoles. We predict that BICs are completely robust to changes in lattice parameters remaining pinned to specific…
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…
Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states.…
We explore the dynamical response of the free surface of an ultra-soft solid driven by a localized moving pressure disturbance. Experiments reveal a steady V-shaped wake analogous to a surface Mach wedge. A simple geometric argument…
We present a class of mechanical lattices based on elliptical gears with quasiperiodic modulation and geometric nonlinearity, capable of exhibiting topologically protected modes and amplitude-driven transitions. Starting from a…
Topological insulators are studied via tight-binding approximations of longitudinally driven photonic lattices with three lattice sites per unit cell. Two cases are considered in detail: Lieb and Kagome lattices. The lattice is decomposed…
We consider a linearly thermoelastic composite medium,which consists of a homogeneous matrix containing a statistically inhomogeneous random set of inclusions, when the concentration of the inclusions is a function of the coordinates…
Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…
Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological…
We analyse the massless wave equation on a class of two dimensional manifolds consisting of an arbitrary number of topological cylinders connected to one or more topological spheres. Such manifolds are endowed with a degenerate…
Topological phases of matter have been widely studied for their robustness against impurities and disorder. The broad applicability of topological materials relies on the reliable transition from idealized, mathematically perfect models to…
It is well known that the bulk physics of a topological phase constrains its possible edge physics through the bulk-edge correspondence. Therefore, the different types of edge theories that a topological phase can host constitute a…