Related papers: Topological Dynamics and Correspondences in Compos…
The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of topological band…
As the counterpart of Hermitian nodal structures, the geometry formed by exceptional points (EPs), such as exceptional lines (ELs), entails intriguing spectral topology. We report the experimental realization of order-3 exceptional lines…
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…
The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers. Here…
Exceptional points (EPs) has seen substantial advances in both experiment and theory. However, in quantum systems, higher-order exceptional points remain of great interest and possess numerous intriguing properties yet to be fully explored.…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic…
Electronic topological phases of matter, characterized by robust boundary states derived from topologically nontrivial bulk states, are pivotal for next-generation electronic devices. However, understanding their complex quantum phases,…
In this paper we explore the effects of quasiperiodicity in paradigmatic models of Chern insulators. We identify a plethora of topological phase transitions and characterize them based on spectral and localization properties. Contrary to…
We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on surfaces within the framework of Nakajima's oscillator algebra. This leads to an identification…
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…
The topology in different dimensions has attracted enormous interests, e.g. the Zak phase in 1D systems, the Chern number in 2D systems and the Weyl points or nodal lines in the systems with higher dimensions. It would be fantastic to find…
The topological classification of energy bands has laid the groundwork for the discovery of various topological phases of matter in recent decades. While this classification has traditionally focused on real-energy bands, recent studies…
The conventional topological description given by the fundamental group of nematic order parameter does not adequately explain the entangled defect line structures that have been observed in nematic colloids. We introduce a new topological…
Topological invariants such as Chern classes are by now a standard way to classify topological phases. Introducing and varying parameters in such systems leads to phase diagrams, where the Chern classes may jump when crossing a critical…
Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several…
In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that…
Topological quantum phase transitions in superconductivity are discussed on two dimensional lattices. The main focus is on the Chern number for superconducting states. Each superconductivity is characterized by the Chern number, and the…
Weyl semimetals and higher-order topological insulators represent two fundamental yet distinct classes of topological matter. While both have been extensively studied in classical-wave systems, their coexistence and controllable transition…
The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner…