Related papers: Topological Euler class as a dynamical observable …
The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling…
We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, an orientation-preserving leafwise…
We introduce and study new interacting topological states that arise in time-reversal symmetric bands with an underlying obstruction to forming localized states. If the $U(1)$ valley symmetry linked to independent charge conservation in…
We critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems, like e.g., the topology of potential energy sub-manifolds (PES). This topological…
We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…
Recent breakthroughs in hyperbolic lattices have expanded the study of topological phases of matter from Euclidean to non-Euclidean spaces. However, prior work has mostly focused on spatial topological states at the single outer edge of…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless $\mathcal{P}\mathcal{T}$ symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases…
Chiral symmetry on bipartite lattices with different numbers of $A$-sites and $B$-sites is exceptional in condensed matter, as it gives rise to zero-energy flat bands. Crystalline systems featuring chiral symmetry with non-equal sublattices…
Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in…
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…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
A common wisdom about quantum many-body systems is that emergent phases typically fall into either the Landau-Ginzburg paradigm or topological classifications. Experimentally realizing the intertwined emergence of spontaneous symmetry…
We explore the gapless topological phases of a $p$-wave superconductor, probing its rich topologically ordered phases and underlying quantum phenomena. The topological order of the system is characterized by studying its entanglement…
The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here…
We construct new stationary weak solutions of the 3D Euler equation with compact support. The solutions, which are piecewise smooth and discontinuous across a surface, are axisymmetric with swirl. The range of solutions we find is different…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
In this study, a tight-binding model on square octagon lattice with nearest-neighbour and next-nearest-neighbour hoppings is considered. The system is topologically trivial although it exhibits quadratic band-touching points in its…
Two-dimensional topological insulators protected by nonlocal symmetries or with fragile topology usually do not admit robust in-gap edge modes due to the incompatibility between the symmetry and the boundary. Here, we show that in a…
Topological phases of matter are generally characterized by topological properties of energy bands of a system. Their transitions under preserved symmetries occur through closing a gap of energy bands, leading to topologically protected…