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Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…
The synthetic Floquet lattice, generated by multiple strong drives with mutually incommensurate frequencies, provides a powerful platform for the quantum simulation of topological phenomena. In this study, we propose a 4-band tight-binding…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
The interplay among topology, disorder, and non-Hermiticity can induce some exotic topological and localization phenomena. Here we investigate this interplay in a two-dimensional non-Hermitian disordered Chern-insulator model with two…
We have studied the dynamical thermal effects on the protected end states of a topological insula- tor (TI) when it is considered as an open quantum system in interaction with a noisy environment at a certain temperature T . As a result, we…
We present a novel class of topological insulators, termed the Takagi topological insulators (TTIs), which is protected by the sublattice symmetry and spacetime inversion ($\mathcal P\mathcal T$) symmetry. The required symmetries for the…
We construct new many-body invariants for 2d Chern and 3d chiral hinge insulators, which are characterized by quantized pumping of dipole and quadrupole moments. The invariants that we devise are written entirely in terms of many-body…
A 3d electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is…
Using density functional theory calculations with a Hubbard $U$, we explore topologically nontrivial phases in $X_2$O$_3$ honeycomb layers with $X=$ $4d$ and $5d$ cation inserted in the band insulator $\alpha$-Al$_2$O$_3$ along the…
Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here,…
Hermitian theories play a major role in understanding the physics of most phenomena. It has been found only in the past decade that non-Hermiticity enables unprecedented effects such as exceptional points, spectral singularities and bulk…
Topological insulators are a new class of insulators in which a bulk gap for electronic excitations is generated by strong spin orbit coupling. These novel materials are distinguished from ordinary insulators by the presence of gapless…
Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI)…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
We study positions of chiral hinge states in higher-order topological insulators (HOTIs) with inversion symmetry. First, we exhaust all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with…
Three dimensional (3D) topological insulators (TIs) are an important class of materials with applications in electronics, spintronics and quantum computing. With the recent development of truly bulk insulating 3D TIs, it has become possible…
In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected…
Topological band insulators which are dynamically generated by electron-electron interactions have been the- oretically proposed in two and three dimensional lattice models. We present evidence that the two-dimensional version can be…
Recently, correlated physics such as superconductivity and insulator at commensurate fractional electron fillings has been discovered in several different systems with Moire superlattice and narrow electron bands near charge neutrality.…
We analytically and numerically analyze the one-dimensional "thin-torus" limit of Fractional Topological Insulators in a series of simple models exhibiting exactly flat bands with local hopping. These models are the one-dimensional limit of…