Related papers: Three-dimensional spinless Euler insulators with r…
In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a…
Real band topology often appears in systems with space-time inversion symmetry and is characterized by invariants such as the Euler and second Stiefel-Whitney classes. Here, we examine the generic band topology of Bogoliubov de-Gennes (BdG)…
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…
Two-dimensional Euler insulators are novel kind of systems that host multi-gap topological phases, quantified by a quantised first Euler number in their bulk. Recently, these phases have been experimentally realised in suitable…
Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a…
We present a series of models of three-dimensional rotation-symmetric fragile topological insulators in class AI (time-reversal symmetric and spin-orbit-free systems), which have gapless surface states protected by time-reversal ($T$) and…
We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal ($\mathcal{PT}$) inversion symmetry. These phases may also host subdimensional…
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic…
We report the theoretical prediction and experimental observation of a new class of four-dimensional (4D) tensor singularities and their three-dimensional (3D) Euler-class descendants, protected by chiral and spacetime inversion symmetries…
We propose an unconventional bulk-edge correspondence for two-dimensional Stiefel-Whitney insulators and Euler insulators, which are topological insulators protected by the $PT$ symmetry. We find that, although the energy spectrum under the…
We study translationally-invariant insulators with inversion symmetry that fall outside the established classification of topological insulators. These insulators are not required to have gapless boundary modes in the energy spectrum.…
In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a…
In this lecture for the Nobel symposium, we review previous research on a class of translational-invariant insulators without spin-orbit coupling. These may be realized in intrinsically spinless systems such as photonic crystals and…
Two-dimensional systems with $C_{2}\mathcal{T}$ ($P\mathcal{T}$) symmetry exhibit the Euler class topology $E\in\mathbb{Z}$ in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying…
We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants protected by space-time inversion symmetry. This finding stands in marked contrast to the conventional…
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry.…
The Euler number is a new topological number recently debuted in the topological physics. Unlike the Chern number defined for a band, it is defined for interbands. We propose a simple model realizing the topological Euler insulator for the…
We study the homotopy classification of symmetry representations to describe the bulk topological invariants protected by the combined operation of a two-fold rotation $C_{2z}$ and time-reversal $T$ symmetries. We define topological…
We construct smooth axisymmetric-with-swirl initial data in a periodic cylinder for which the three-dimensional incompressible Euler evolution develops a finite-time boundary singularity. The construction is carried out in the dynamically…
We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…