Related papers: Topologically localized insulators
We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial"…
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,…
We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct…
Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…
We show that there exist two dimensional (2D) time reversal invariant fractionalized insulators with the property that both their boundary with the vacuum and their boundary with a topological insulator can be fully gapped without breaking…
Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…
We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two and three dimensional crystalline HOT insulators, accommodating topological corner states, we…
Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…
Dimensional evolution between one- ($1D$) and two-dimensional ($2D$) topological phases is investigated systematically. The crossover from a $2D$ topological insulator to its $1D$ limit shows oscillating behavior between a $1D$ ordinary…
Floquet topological insulators are topological phases of matter generated by the application of time-periodic perturbations on otherwise conventional insulators. We demonstrate that spatial variations in the time-periodic potential lead to…
Of the available classes of insulators which have been shown to contain topologically non-trivial properties one of the most important is class AII, which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$ This class…
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field…
We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in…
We study a general problem how the gap in a nonmagnetic band insulator closes by tuning a parameter. We review our recent results on the classification of all the possible gap closing in two and three dimensions. We show that they accompany…
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic…
The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, the topology of the axion insulator stays robust, and an…
We apply ideas from $C^*$-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological…
Topological insulators are a class of band insulators with non-trivial topology, a result of band inversion due to the strong spin-orbit coupling. The transition between topological and normal insulator can be realized by tuning the…
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant…