Related papers: Structural Disorder Induced Second-order Topologic…
One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial…
Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order…
The topological phase in amorphous systems adds a new dimension to the topological states of matter. Here, we present an interesting phenomenon dubbed the topological Anderson amorphous insulator (TAAI). Anderson disorder can drive…
Symmetry and topology are essential principles in topological physics. Recently, the idea of sub-symmetry-protected topology -- where some of the original symmetries are broken while a remaining subset, called sub-symmetries, continues to…
We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions, these states of matter are generally characterized by the…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…
Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators…
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…
The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional…
We study three dimensional systems where strong repulsion leads to an insulating state via spontaneously generated spin-orbit interactions. We discuss a microscopic model where the resulting state is topological. Such topological `Mott'…
Topological phases of matter are classified based on symmetries, with nonsymmorphic symmetries like glide reflections and screw rotations being of particular importance in the classification. In contrast to extensively studied glide…
A second-order topological insulator in $d$ dimensions is an insulator which has no $d-1$ dimensional topological boundary states but has $d-2$ dimensional topological boundary states. It is an extended notion of the conventional…
Second-order topological insulators (SOTIs) are the topological phases of matter in d dimensions that manifest (d-2)-dimensional localized modes at the intersection of the edges. We show that SOTIs can be designed via stacked Chern…
A $d$-dimensional second-order topological insulator (SOTI) can host topologically protected $(d - 2)$-dimensional gapless boundary modes. Here we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to…
Recent breakthrough on topological Anderson insulators revealed the breakdown of the traditional perception that sufficiently strong disorder may induce the appearance of topological protected transport states instead of destruction.…
Band insulators appear in a crystalline system only when the filling -- the number of electrons per unit cell and spin projection -- is an integer. At fractional filling, an insulating phase that preserves all symmetries is a Mott…
We introduce a novel class of interaction-enabled topological crystalline insulators in two- and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the…
Topological insulators (TI) are a phase of matter that host unusual metallic states on their surfaces. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected…