Related papers: Revealing Topology in Metals using Experimental Pr…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
Topological materials host fascinating low dimensional gapless states at the boundary. As a prominent example, helical topological edge states (TESs) of two-dimensional topological insulators (2DTIs) and their stacked three-dimensional (3D)…
In recent years, realizing new topological phase of matter has been a hot topic in the fields of physics and materials science. Topological semimetals and metals can conventionally be classified into two types: type-I and type-II according…
In chiral crystals crystalline symmetries can protect multifold fermions, pseudo-relativistic masless quasiparticles that have no high-energy counterparts. Their realization in transition metal monosilicides has exemplified their intriguing…
We show that hybrid structures of topological insulators and materials without topological protection can be employed to create perfectly conducting channels hosted in the non-topological part. These states inherit the topological…
The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…
In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…
Higher-order topological states (HOTS) have been extensively investigated in classical wave systems. They do not exist in the band gaps of infinite materials, while exhibit as the in-gap localized modes once the infinite materials are…
Conventional metals, insulators, and semimetals are constrained by fundamental limitations in terms of their thermoelectric performance. Topological materials offer certain features that allow them to circumvent these constraints, and…
The classification of gapped phases of non-interacting fermions hinges on the tenfold symmetries and on the spatial dimension. The notion of dimension leads to a well defined demarcation between bulk and edge. Here we explore the nature of…
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…
We propose and analyze a scheme to observe topological phenomena with ions in microtraps. We consider a set of trapped ions forming a regular structure in two spatial dimensions and interacting with lasers. We find phonon bands with…
In this paper topological $K$-group calculations for fiber bundles with structure group $SO(3)$ over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is…
The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe which directly couples to an exotic…
In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…
The discovery of topological insulators and semimetals has opened up a new perspective to understand materials. Owing to the special band structure and enlarged Berry curvature, the linear responses are strongly enhanced in topological…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
Symmetry plays a major role in all disciplines of physics. Within the field of topological materials there is a great interest in understanding how the mechanics of crystalline and internal symmetries protect crossings between the…
Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While…
Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic laser-assisted…