相关论文: Observation of an acoustic topological Euler insul…
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…
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 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 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…
The study of topological band theory in classical structures has led to the development of novel topological metamaterials with intriguing properties. While single-gap topologies are well understood, recent novel multi-gap phases have…
Non-Abelian topological phases, which go beyond traditional Abelian topological band theory, are garnering increasing attention. This is further spurred by periodic driving, leading to predictions of many novel multi-gap Floquet topological…
Although topological materials have recently seen tremendous development, their applications have remained elusive. Simultaneously, there exists considerable interest in pushing the limits of topological materials, including the exploration…
Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…
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…
Topological phases of matter span a wide area of research shaping fundamental pursuits and offering promise for future applications. While a significant fraction of topological materials has been characterized using symmetry requirements of…
Braiding has attracted significant attention in physics because of its important role in describing the fundamental exchange of particles. Infusing the braiding with topological protection will make it robust against imperfections and…
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…
Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
A general and beautiful picture for the realization of topological insulators is that the mass term of the Dirac model has a nodal surface wrapping one Dirac point. We show that this geometric picture based on Dirac points can be…
Topological features embedded in ancient braiding and knotting arts endow significant impacts on our daily life and even cutting-edge science. Recently, fast growing efforts are invested to the braiding topology of complex Bloch bands in…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
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…
Existence of robust edge modes at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, topological insulators. Such electronic states were originally predicted…
Braiding is a geometric concept that manifests itself in a variety of scientific contexts from biology to physics, and has been employed to classify bulk band topology in topological materials. Topological edge states can also form braiding…