Related papers: Classifying topological floppy modes in the contin…

Three-dimensional Weyl fermions are found to emerge from simple cubic lattices with staggered fluxes. The mechanism is to gap the quadratic band touching by time-reversal-symmetry-breaking hoppings. The system exhibits rich phase diagrams…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

We investigate a novel higher-order topological behavior in elastic lattices characterized by nonsymmorphic symmetries. In the theoretical spring-mass lattice, altering the vertex mass allows for fine-tuning of the topological features…

A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are considered. Time-reversal symmetry is broken by…

The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. On the other hand, very little is known…

We provide a manifestly topological classification scheme for generalised Weyl semimetals, in any spatial dimension and with arbitrary Weyl surfaces which may be non-trivially linked. The classification naturally incorporates that of Chern…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

Spin fluctuations in two-dimensional (2D) ferromagnets in the presence of crystalline lattice dislocations are investigated. We show the existence of topologically protected non-propagative modes that localize at dislocations. These in-gap…

For conformal field theories which admit a dual gravitational description in anti-de Sitter space, electrical transport properties, such as conductivity and charge diffusion, are determined by the dynamics of a U(1) gauge field in the bulk…

We discuss gauge theories of the Yang-Mills kind in finite regions with boundaries, and in particular the definition of the corresponding quasi-local degrees of freedom and their gluing upon composition of the underlying regions. Although…

We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the…

We show that Hall conductance and its non-abelian and higher-dimensional analogs are obstructions to promoting a symmetry of a state to a gauge symmetry. To do this, we define a local Lie algebra over a Grothendieck site as a pre-cosheaf of…

In recent years there has been a great interest in topological photonics and protected edge states. Here, we present a first principles method to compute topological invariants of three-dimensional gapless phases. Our approach allows to…

We present a general analysis of two-dimensional optical lattice models that give rise to topologically non-trivial insulating states. We identify the main ingredients of the lattice models that are responsible for the non-trivial…

We study the elasticity of random fiber networks. Starting from a microscopic picture of the non-affine deformation fields we calculate the macroscopic elastic moduli both in a scaling theory and a self-consistent effective medium theory.…

Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological…

Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…

Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly…

We provide an exact analytical technique to obtain within a lattice model the wave functions of the edge states in zigzag- and bearded-edge graphene, as well as of the Fermi-arc surface states in Weyl semimetals described by a minimal bulk…

Topological band theory has been studied for free fermions for decades, and one of the most profound physical results is the bulk-boundary correspondence. Recently a focus in topological physics is extending topological classification to…