Related papers: Second-order topological insulators and supercondu…
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…
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…
We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by non-interacting Bloch and Bogoliubov de Gennes…
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 classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${\bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we…
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…
We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only…
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…
Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have…
Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery…
Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological…
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of…
Higher order topological insulators are a new class of topological insulators in dimensions $\rm d>1$. These higher-order topological insulators possess $\rm (d - 1)$-dimensional boundaries that, unlike those of conventional topological…
Point-gap topological phases of non-Hermitian systems exhibit exotic boundary states that have no counterparts in Hermitian systems. Here, we develop classification of second-order point-gap topological phases protected by reflection…
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…
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…
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…
A Z2 topological insulator protected by time-reversal symmetry is realized via spin-orbit interaction driven band inversion. For example, the topological phase in the Bi-Sb system is due to an odd number of band inversions. A related…
Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the…
Second-order photonic topological insulators that host highly localized corner states resilient to defects, are opening new routes towards developing fascinating photonic devices. However, the existing works on second-order photonic…