Related papers: Topological Mirror Insulators in One Dimension
The possibility of realizing topological insulators by spontaneous formation of electronic superstructure is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a…
Recent topological band theory distinguishes electronic band insulators with respect to various symmetries and topological invariants, most commonly, the time reversal symmetry and the $\rm Z_2$ invariant. The interface of two topologically…
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…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
The relation between bulk topological invariants and experimentally observable physical quantities is a fundamental property of topological insulators and superconductors. In the case of chiral symmetric systems in odd spatial dimensions…
Higher-order topological insulators have triggered great interests because of exhibitions of non-trivial bulk topology on lower-dimensional boundaries like corners and hinges. While such interesting phases have been investigated in a…
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…
A two-legged ladder model, one dimensional, exhibiting the parity anomaly is constructed. The model belongs to the $C$ and $CI$ symmetry classes, depending on the parameters, but, due to reflection, it exhibits topological insulation. The…
The axion insulator exhibits a topological magnetoelectric effect characterized by an axion angle $\theta=\pi$, while the time-reversal-doubled axion insulator (T-DAXI) can be viewed as two copies of an axion insulator related by…
We study interaction effects on the topological crystalline insulators protected by time-reversal ($T$) and reflection symmetry ($R$) in two and three spatial dimensions. From the stability analysis of the edge states with bosonization, we…
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with…
We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of noncommutative index theory of operator algebras. In…
We provide an index-theoretic proof of the bulk-boundary correspondence for two- and three-dimensional second-order topological insulators that preserve inversion symmetry, which are modeled as rectangles and rectangular prism-shaped…
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 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…
Time-reversal-invariant topological superconductors have a full paring gap in the bulk and gapless Majorana states at the edge or on the surface. Here, we theoretically propose topological superconductivity in a doped quantum spin Hall…
A concrete strategy is presented for generating strong topological insulators in $d+d'$ dimensions which have quantized physics in $d$ dimensions. Here, $d$ counts the physical and $d'$ the virtual dimensions. It consists of seeking…
We study three dimensional insulators with inversion symmetry, in which other point group symmetries, such as time reversal, are generically absent. Their band topology is found to be classified by the parities of occupied states at time…
Photonic platforms invariant under parity ($\mathcal{P}$), time-reversal ($\mathcal{T}$), and duality ($\mathcal{D}$) can support topological phases analogous to those found in time-reversal invariant ${\mathbb{Z}_2}$ electronic systems…
Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn…