Related papers: Model-free characterization of topological edge an…
We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry protected topological phases. This is possible even without gapped degrees of freedom in the bulk ---in…
Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…
Topological materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on…
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…
Symmetry-protected topological phases cannot be described by any local order parameter and are beyond the conventional symmetry-breaking paradigm for understanding quantum matter. They are characterized by topological boundary states robust…
The discovery of the topological insulators has fueled a surge of interests in the topological phases in periodic systems. Topological insulators have bulk energy gap and topologically protected gapless edge states. The edge states in…
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…
Nonlinear topology has been much less inquired compared to its linear counterpart. Existing advances have focused on nonlinearities of limited magnitudes and fairly homogeneous types. As such, the realizations have rarely been concerned…
Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that $\mathbb{Z}_N$ Berry phase (Berry phase quantized into $2\pi/N$) is a useful tool…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
The vast majority of symmetry-protected topological (SPT) states are difficult to detect, which often leads to their misidentification as ordinary or topologically trivial phases. In this work, we propose a general framework for detecting…
The continuous effort towards topological quantum devices calls for an efficient and non-invasive method to assess the conformity of components in different topological phases. Here, we show that machine learning paves the way towards…
Topological edge states in electromagnetic systems feature a set of attracting fundamental properties and unveil prospective applications based on disorder robustness and tailored localization. Despite active efforts in implementing…
Topological phases have been explored in various fields in physics such as spintronics, photonics, liquid helium, correlated electron system and cold-atomic system. This leads to the recent foundation of emerging materials such as…
Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial…
Topological insulators are described by topological invariants that can be computed by integrals over momentum space, but also as traces over local, real-space topological markers. These markers are useful to detect topological insulating…
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological…
Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…