Related papers: Topological Crystalline Insulators
A general and beautiful picture for the realization of topological insulators is that the mass term of the Dirac model has a nodal surface wrapping one Dirac point. We show that this geometric picture based on Dirac points can be…
We formulate topological crystalline materials on the basis of the twisted equivariant $K$-theory. Basic ideas of the twisted equivariant $K$-theory is explained with application to topological phases protected by crystalline symmetries in…
In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological…
In this review, We discussed the theoretical foundation and experimental discovery of different topological electronic states of material in condensed matter. At first, we briefly reviewed the conventional electronic states, which have been…
Recent years saw the complete classification of topological band structures, revealing an abundance of topological crystalline insulators. Here we theoretically demonstrate the existence of topological materials beyond this framework,…
Using a tight-binding approach we study theoretically the nature of surface states in Pb0.4Sn0.6Te - the newly discovered topological-crystalline-insulator. Apart from the studied before (001) surface states, two other surface families,…
We present a series of models of three-dimensional rotation-symmetric fragile topological insulators in class AI (time-reversal symmetric and spin-orbit-free systems), which have gapless surface states protected by time-reversal ($T$) and…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these "higher-order" boundary states…
Exponentially localized surface states are the most distinctive property of a crystal with non-trivial band topology. Such surface states play a key role in characterizing topological insulators (TIs), both in theory and experiments. TIs…
It has been known that an anti-unitary symmetry such as time-reversal or charge conjugation is needed to realize Z2 topological phases in non-interacting systems. Topological insulators and superconducting nanowires are representative…
The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been…
In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases…
Three-dimensional higher-order topological semimetals in crystalline systems exhibit higher-order Fermi arcs on one-dimensional hinges, challenging the conventional bulk-boundary correspondence. However, the existence of higher-order Fermi…
Topological insulators [1-6] is a new quantum phase of matter with exotic properties such as dissipationless transport and protection against Anderson localization [7]. These new states of quantum matter could be one of the missing links…
We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…
Topological insulators are newly discovered materials with the defining property that any boundary cut into such crystal supports spectrum which is immune to the Anderson localization. The present paper summarizes our efforts on the…
Discrete degrees of freedom, such as spin and orbital, can provide intriguing strategies to manipulate electrons, photons, and phonons. With a spin degree of freedom, topological insulators have stimulated intense interests in…
We investigate the spin and charge densities of surface states of the three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum description of the material [Zhang {\em et al.}, Nat. Phys. 5, 438 (2009)]. The spin…