Related papers: Classifying topological floppy modes in the contin…
Recent developments in topological mechanics have demonstrated the ability of Maxwell lattices to effectively focus stress along domain walls between differently polarized domains. The focusing ability can be exploited to protect the…
The study of Weyl points in electronic systems has inspired many recent researches in classical systems such as photonic and acoustic lattices. Here we show how the Weyl physics can also inspire the design of novel elastic structures. We…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
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.…
Topology describes global quantities invariant under continuous deformations, such as the number of elementary excitations at a phase boundary, without detailing specifics. Conversely, differential laws are needed to understand the physical…
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and…
Granular matter at the jamming transition is poised on the brink of mechanical stability, and hence it is possible that these random systems have topologically protected surface phonons. Studying two model systems for jammed matter, we find…
Weyl semimetals typically appear in systems in which either time-reversal (T) or inversion (P}) symmetry are broken. Here we show that in the presence of gauge potentials these topological states of matter can also arise in fermionic…
The engineering of synthetic materials characterised by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial…
The presence of a topological phase in a topological many-body system can be distinguished through the analysis of topological invariants. In the present study, the topological invariants for the strongly coupled holographic semimetals have…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk-edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such…
We propose a new version of Wigner-Weyl calculus for tight-binding lattice models. It allows to express various physical quantities through Weyl symbols of operators and Green's functions. In particular, Hall conductivity in the presence of…
Topological phononics extends the foundational concepts of topological condensed matter physics to the realm of lattice vibrations and classical mechanical waves, unlocking robust, defect-immune states and phenomena beyond the reach of…
We address the co-existence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well known Bernevig-Hughes-Zhang model to introduce a smooth function…
We present fracturing analysis of topological Maxwell lattices when they are stretched by applied stress. Maxwell lattices are mechanical structures containing equal numbers of degrees of freedom and constraints in the bulk and are thus on…
We find a series of topological phase transitions in a half-metal/superconductor heterostructure, by tuning the direction of the magnetization of the half-metal film. These include transitions between a topological superconducting phase…
The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in…