Related papers: Three-dimensional spinless Euler insulators with r…

Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…

We identify a topological Z index for three dimensional chiral insulators with P*T symmetry where two Hamiltonian terms define a nodal loop. Such systems may belong in the AIII or DIII symmetry class. The Z invariant is a winding number…

We introduce a Legendrian invariant built out of the Turaev torsion of generating families. This invariant is defined for a certain class of Legendrian submanifolds of 1-jet spaces, which we call of Euler type. We use our invariant to study…

In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…

Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The…

Electronic bands in systems with space-time inversion (IST) symmetry can host nontrivial Euler topology. Here, we investigate the band topology of IST-symmetric superconducting honeycomb lattices and demonstrate that s-wave spin-singlet…

We present a self-contained interior quadrupole mechanism for finite-time singularity formation in the axisymmetric three-dimensional incompressible Euler equations with swirl in the whole space. The construction is localized away from the…

We derive a $\mathbb{Z}_4$ topological invariant that extends beyond symmetry eigenvalues and Wilson loops and classifies two-dimensional insulators with a $C_4 \mathcal{T}$ symmetry. To formulate this invariant, we consider an irreducible…

For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological…

B\'ezout's theorem, nonequivariantly, can be interpreted as a calculation of the Euler class of a sum of line bundles over complex projective space, expressing it in terms of the rank of the bundle and its degree. We give here a…

A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…

Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy…

Recently, correlated physics such as superconductivity and insulator at commensurate fractional electron fillings has been discovered in several different systems with Moire superlattice and narrow electron bands near charge neutrality.…

Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of…

Combings of oriented compact 3-manifolds are homotopy classes of nowhere zero vector fields in these manifolds. A first known invariant of a combing is its Euler class, that is the Euler class of the normal bundle to a combing…

The Bloch band theory and Brillouin zone (BZ) that characterize wave behaviors in periodic mediums are two cornerstones of contemporary physics ranging from condensed matter to topological physics. Recent theoretical breakthrough revealed…

The local Euler obstructions and the Euler characteristics of linear sections with all hyperplanes on a stratified projective variety are key geometric invariants in the study of singularity theory. Despite their importance, in general it…

One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss…

We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the…

It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on…