Related papers: Optical manifestations and bounds of topological E…
The Euler class characterizes the topology of two real bands isolated from other bands in two-dimensions. Despite various intriguing topological properties predicted up to now, the candidate real materials hosting electronic Euler bands are…
Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of crystalline metals with…
Non-Abelian states of matter, in which the final state depends on the order of the interchanges of two quasiparticles, can encode information immune from environmental noise with the potential to provide a robust platform for topological…
While the landscape of free-fermion phases has drastically been expanded in the last decades, recently novel multi-gap topological phases were proposed where groups of bands can acquire new invariants such as Euler class. As in conventional…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of…
Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in non-Hermitian parity-time symmetric systems, where the topological invariant remains conserved,…
The topological Euler characteristic number of the energy band proposed in our previous work (see Yu-Quan Ma et al., arXiv:1202.2397; EPL 103, 10008 (2013)) has been recently experimentally observed by X. Tan et al., Phys. Rev. Lett.…
Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…
The paper considers the Euler system of PDE on a smooth compact Riemannian manifold of positive curvature without boundary, and the sphere ${\mathbb{S}}^2$ in particular. The paper interprets the Euler equations as a transport problem for…
Among different topological and related phases of condensed matter, nodal semimetals occupy a special place - the electronic band topology in these materials is related to three-dimensional bulk, rather than to surface, states. A great…
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…
We establish a mixed observability inequality for a class of degenerate hyperbolic equations on the cylindrical domain $\Omega = \mathbb{T} \times (0,1)$ with mixed Neumann Dirichlet boundary conditions. The degeneracy acts only in the…
In this paper, we study Euler classes in groups of homeomorphisms of Seifert fibered 3-manifolds. We show that, in contrast to the familiar Euler class for $\mathrm{Homeo}_0(S^1)^\delta$, these Euler classes for…
Nodal planes, two-dimensional symmetry-enforced band crossings, can carry a topological charge, similar to Weyl points. While the transport properties of Weyl points are well understood, those of nodal planes remain largely unexplored.…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding…
In systems with a real Bloch Hamiltonian band nodes can be characterised by a non-Abelian frame-rotation charge. The ability of these band nodes to annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps the sign of…
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…
Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can…