Related papers: Cell augmentation framework for topological lattic…
We connect a family of gauge theories (Maxwell theories with a magnetoelectric coupling $\theta = 2 \pi k, k \in \mathbb{Z}$) to the family of 3D topological lattice models introduced by Walker and Wang. In particular, we show that the…
Topological physics opens a door towards flexible routing and resilient localization of waves of various nature. Recently proposed higher-order topological insulators provide advanced control over wave localization in the structures of…
Topological surface states are unique to topological materials and are immune to disturbances. In isostatic lattices, mechanical topological floppy modes exhibit softness depending on the polarization relative to the terminating surface.…
Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the…
A discrete-to-continuum transformation to model 2-D discrete lattices as energetically equivalent 1-D continuum beams is developed. The study is initiated in a classical setting but results in a non-classical two-scale micropolar beam model…
Topological states can be used to control the mechanical properties of a material along an edge or around a localized defect. The surface rigidity of elastic networks is characterized by a bulk topological invariant called the polarization;…
Topological mechanical structures exhibit robust properties protected by topological invariants. In this letter, we study a family of deformed square lattices that display topologically protected zero-energy bulk modes analogous to the…
The two pillars of Algebraic topology - Homology and homotopy theory rely on the availability of basic building blocks called cells. Cells take the form of simplexes, and have properties such as faces, sub-cells, convexity and…
Topological insulators subject to a time-symmetry-breaking perturbation are predicted to display a magneto-electric effect that causes the electric and magnetic induction fields to mix at the material's surface. This effect induces…
We investigate the dispersion topology of elastic lattices characterized by spatial stiffness modulation. The modulation is defined by the sampling of a two-dimensional surface, which provides the lattices with topological properties that…
Strong light-matter interaction enriches topological photonics by dressing light with matter, which provides the possibility to realize tuneable topological devices with immunity to defects. Topological exciton polaritons, half-light…
Topological concepts have been applied to a wide range of fields in order to successfully describe the emergence of robust edge modes that are unaffected by scattering or disorder. In photonics, indications of lasing from topologically…
In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different…
The rich physical properties of multiatomic molecules and crystalline structures are determined, to a significant extent, by the underlying geometry and connectivity of atomic orbitals. This orbital degree of freedom has also been used…
Exhaustive study of topological semimetal phases of matter in equilibriated electonic systems and myriad extensions has built upon the foundations laid by earlier introduction and study of the Weyl semimetal, with broad applications in…
Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a…
We are interested in expanding our understanding of symplectic matroids by exploring the properties of a class of symplectic matroids with a "lattice of flats". Taking a well-behaved family of subdivisions of the cross polytope we obtain a…
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…
In this, the third paper in our series describing the excitations of the higher lattice gauge theory model for topological phases, we will examine the 3+1d case in detail. We will explicitly construct the ribbon and membrane operators which…
Transistor topology optimization is a critical step in standard cell design, directly dictating diffusion sharing efficiency and downstream routability. However, identifying optimal topologies remains a persistent bottleneck, as…