Related papers: Local Topological Markers in Odd Dimensions

Conventional Chern insulators are two-dimensional periodic structures that support unidirectional edge states at the boundary, while the wave propagation in the bulk regions is forbidden. The number of unidirectional edge states is governed…

We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show…

We establish the theory of critical transport in amorphous Chern insulators and show that it lies beyond the current paradigm of topological criticality epitomized by the quantum Hall transitions. We consider models of Chern insulators on…

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…

Topological invariants in the band structure, such as Chern numbers, are crucial for the classification of topological matters and dictate the occurrence of exotic properties, yet their direct spectroscopic determination has been largely…

We investigate the topological phase transition with large Chern number in a coupled layer system. The topological transitions between different topological superfluids can be realized by controlling the binding energy, interlay tunneling…

The Chern number, as a topological invariant, characterizes the topological features of a 2D system and can be experimentally detected through Hall conductivity. In this work, we investigate the connection between the Chern number and the…

Particles hopping on a two-dimensional hyperbolic lattice feature unconventional energy spectra and wave functions that provide a largely uncharted platform for topological phases of matter beyond the Euclidean paradigm. Using real-space…

Topological insulators (TIs) are a new quantum state of matter discovered recently, which are characterized by unconventional bulk topological invariants. Proposals for practical applications of the TIs are mostly based upon their metallic…

We construct theoretical models for two dimensional(2d) chiral $d_{x^2-y^2}\pm id_{xy}$ topological superconductors and for three dimensional(3d) $d$ wave topological superconductors. Moreover we build models for any 2d class C and 3d class…

Topological states of matter emergent as a new type of quantum phases, which can be distinguished by their associated topological invariants, e.g., Chern numbers. Currently, there is increasing in-terests toward the physically detection of…

Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk…

The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a…

Motivated by recent developments in quantum simulation of synthetic dimensions, e.g. in optical lattices of ultracold atoms, we discuss here $d$-dimensional periodic, gapped quantum systems for $d \le 4$, with focus on the topology of the…

Local topological charge structure in the 2D CP(N-1) sigma models is studied using the overlap Dirac operator. Long-range coherence of topological charge along locally 1D regions in 2D space-time is observed. We discuss the connection…

Photonic systems provide a highly tunable platform for emulating quantum Hall physics. This tunability enables probing of the interplay between strong disorder and robust topological transport that remains difficult to access in solid-state…

A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for…

We analyse the topological transition and localization evolution of disordered two dimensional systems with non trivial topology based on bipartite lattices. Chern insulators with broken time reversal symmetry show non standard behavior for…

Topological insulator-based methods underpin the topological classification of gapped bands, including those surrounding semi-metallic nodal defects. However, multiple bands with gap-closing points can also possess non-trivial topology. We…

In disordered two dimensional Chern insulators, a single bulk extended mode is predicted to exist per band, up to a critical disorder strength; all the other bulk modes are localized. This behavior contrasts strongly with topologically…