Related papers: Statistical Topological Insulators
Topological insulators are new quantum states with helical gapless edge or surface states inside the bulk band gap.These topological surface states are robust against the weak time-reversal invariant perturbations, such as lattice…
We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…
The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point…
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…
An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a…
It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize when the bulk correlation length diverges.…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of…
Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states…
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…
We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that…
Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with…
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of…
Topological insulators are solid state systems of independent electrons for which the Fermi level lies in a mobility gap, but the Fermi projection is nevertheless topologically non-trivial, namely it cannot be deformed into that of a normal…
We show that compositions of time-reversal and spatial symmetries, also known as the magnetic-space-group symmetries, protect topological invariants as well as surface states that are distinct from those of all preceding topological states.…
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…
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 work, we identify a new class of Z2 topological insulator protected by non-symmorphic crystalline symmetry, dubbed a "topological non-symmorphic crystalline insulator". We construct a concrete tight-binding model with the…
Topological crystalline insulators define a new class of topological insulator phases with gapless surface states protected by crystalline symmetries. In this work, we present a general theory to classify topological crystalline insulator…
Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the lattice. Here, we experimentally demonstrate that the topological…