Related papers: Colloquium: Topological Band Theory
The theory of symmetry indicators has enabled database searches for topological materials in normal conducting phases, which has led to several encyclopedic topological material databases. To date, such a database for topological…
Recent years have seen multiple high-throughput studies reveal an immense number of topological materials through use of symmetry indicators. Despite this success, three-dimensional topological insulators (TI) admitting a band-gap larger…
Quantum materials are defined by the emergence of new properties resulting from collective quantum effects and by holding promise for their quantum applications. Novel superconductors, from high-Tc cuprates and iron-based superconductors to…
One-dimensional crystals serve as a versatile platform for engineering nontrivial states, which can be easily explored in transport configurations. In this work, we analyze the properties of a periodic structure composed of an H-shaped unit…
A band gap for electronic states in crystals governs various properties of solids, such as transport, optical and magnetic properties. Its estimation and control have been an important issue in solid state physics. The band gap can be…
The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical…
Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of…
Two quintessential ingredients governing the topological invariant of a system are the dimensionality and the symmetry of the system. Due to the recent development of thin film and artificial superstructure growth technique, it is possible…
Topological insulators and topological semimetals are both new classes of quantum materials, which are characterized by surface states induced by the topology of the bulk band structure. Topological Dirac or Weyl semimetals show linear…
Optical lattices are known for their flexibility to emulate condensed matter physics and beyond. Based on an early theoretical proposal [Science Bulletin 65, 2080 (2020)], a recent experiment published by Wang et al. [Science 372, 271…
Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial…
Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the…
Self-propulsion is a quintessential aspect of biological systems, which can induce nonequilibrium phenomena that have no counterparts in passive systems. Motivated by biophysical interest together with recent advances in experimental…
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…
Topological phases, such as Chern insulators, are defined in terms of additive indices that are stable against the addition of trivial degrees of freedom. Such topology presents an obstruction to any Wannier representation, namely, the…
We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological…
The unique properties of spin-polarized surface or edge states in topological insulators (TIs) make these quantum coherent systems interesting from the point of view of both fundamental physics and their implementation in low power…
Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely…
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…
Topological flat bands in two-dimensional (2D) moir\'e materials have emerged as promising platforms for exploring the interplay between topology and correlation effects. However, realistic calculations of moir\'e band topology using…