Related papers: Universal Continuum Theory for Topological Edge So…
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
Maxwell lattice metamaterials possess a rich phase space with distinct topological states featuring mechanically polarized edge behaviors and strongly asymmetric acoustic responses. Until now, demonstrations of non-trivial topological…
A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedure, secondly by taking the long-wavelength limit of…
A collisionless continuous medium in Euclidean space is discussed, i.e. a continuum of free particles moving inertially, without interacting with each other. It is shown that the distribution density of such medium is weakly converging to…
We describe the possibility for topologically robust edge states existing on interfaces of triangular lattices which are supported by rotational symmetries that are sensitive to boundary conditions. Such states are trivial from the…
In these decades, it has been gradually established that edge modes of a wide class of topologically ordered systems are governed by the bulk-edge correspondence and anyon condensation. The former has been studied many times because it can…
We develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of curvature-dependent surface elasticity, we…
We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…
The existence of topologically protected edge modes is often cited as a highly desirable trait of topological insulators. However, these edge states are not always present. A realistic physical treatment of long range hopping in a…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
In the absence of any symmetry constraints we address universal properties of the boundary charge $Q_B$ for a wide class of nearest-neighbor tight-binding models in one dimension with one orbital per site but generic modulations of on-site…
The scope of this Ph.D thesis is to study the effects of the presence of a boundary from a Quantum Field Theoretical perspective, searching for new physics and explanations of observed phenomena. In particular, thanks to the formal QFT…
How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the…
A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological…
Heterogeneous nucleation at surface edges is pervasive across nature and industry, yet the role of line tension, arising from asymmetric capillary interactions at geometric singularities, remains poorly understood. Herein we develop a…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
We study the edge physics of gapped quantum systems in the framework of Projected Entangled Pair State (PEPS) models. We show that the effective low-energy model for any region acts on the entanglement degrees of freedom at the boundary,…
In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…
The recent discoveries about topological insulators have been promoting theoretical and experimental research. In this dissertation, the basic concepts of topological insulators and the Quantum Hall Effect are reviewed focusing the…
The Maxwell-Calladine index theorem plays a central role in our current understanding of the mechanical rigidity of discrete materials. By considering the geometric constraints each material component imposes on a set of underlying degrees…