Related papers: Atomic limit and inversion-symmetry indicators for…
While the symmetry-based diagnosis of topological insulators and semimetals has enabled large-scale discovery of topological materials candidates, the extension of these approaches to the diagnosis of topological superconductors remains a…
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…
We study superconductors with $n$-fold rotational invariance both in the presence and in the absence of spin-orbit interactions. More specifically, we classify the non-interacting Hamiltonians by defining a series of $Z$-numbers for the…
Symmetry indicators are a modern tool for characterizing topological phases that require only minimal computational expense but provide an elegant means of designing practical devices. This paper demonstrates how a rotational symmetry…
We present a detailed study of the gap symmetry and the quasiparticle wave function topology in two-dimensional superconductors without inversion center. The strong spin-orbit coupling of electrons with the crystal lattice makes it…
We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is…
The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to the…
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…
The semimetal-superconductor quantum phase transition on the two-dimensional (2D) surface of a 3D topological insulator is conjectured to exhibit an emergent $\mathcal{N}=2$ supersymmetry, based on a renormalization group (RG) analysis at…
Recent development in exact classification of a superconducting gap has elucidated various unconventional gap structures, which have not been predicted by the classification of order parameter based on the point group. One of the important…
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry.…
In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a…
We extend the previously defined many-body marker for two-dimensional $\mathbb{Z}_2$ topological insulators [I. Gilardoni {\it et al.}, Phys. Rev. B {\bf 106}, L161106 (2022)] to distinguish trivial, weak-, and strong-topological insulators…
While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections…
The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a…
Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five…
We study anomalies in time-reversal ($\mathbb{Z}_2^T$) and $U(1)$ symmetric topological orders. In this context, an anomalous topological order is one that cannot be realized in a strictly $(2+1)$-D system but can be realized on the surface…
We study translationally-invariant insulators with inversion symmetry that fall outside the established classification of topological insulators. These insulators are not required to have gapless boundary modes in the energy spectrum.…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…