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The higher-order topological insulator (HOTI) protected by spacial symmetry has been studied in-depth on models with square lattice. Our work, based on an alternative model on the breathing Kagome lattice, revealed that the different types…
The two-dimensional topological insulator phase has been observed previously in single HgTe-based quantum wells with inverted subband ordering. In double quantum wells (DQWs), coupling between the layers introduces additional degrees of…
The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order…
Recently, high-order topological insulators (HOTIs), accompanied by topologically nontrivial boundary states with codimension larger than one, have been extensively explored because of unconventional bulk-boundary correspondences. As a…
Topological insulator (TI) is an exciting discovery because of its robustness against disorder and interactions. Recently, higher-order TIs have been attracting increasing attention, because they host 1D topologically-protected hinge states…
The higher-order topological insulators (HOTIs), with such as the topological corner states, emerge as a thriving topic in the field of topological physics. But few connections have been found for the HOTIs with the well explored…
Higher-order topological insulators, which support lower-dimensional topological boundary states than the first-order topological insulators, have been intensely investigated in the integer dimensional systems. Here, we provide a new…
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not…
A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear…
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…
Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to…
We propose magnetic second-order topological insulators (SOTIs). First, we study a three-dimensional model. It is pointed out that the previously proposed topological hinge insulator has actually surface states along the [001] direction in…
The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this paper we demonstrate that the existence of a 2D…
Topological insulators (TIs) are characterized by an insulating bulk and symmetry protected bound state on their boundaries. A "strong" topological insulator is characterized by robust conducting states on \emph{all} boundaries protected by…
Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…
Higher-order topological insulators (HOTIs) represent a novel class of topological materials, characterised by the emergence of topological boundary modes at dimensions two or more lower than those of bulk materials. Recent experimental…
A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological…
Higher-order topological insulators harbor unique corner modes that hold immense potential for applications in information storage. However, the practical manipulation of these states has been constrained by the fixed positions and energies…
Higher-order topological~(HOT) states,~hosting topologically protected modes on lower-dimensional boundaries,~such as hinges and corners, have recently extended the realm of the static topological phases.~Here we demonstrate the possibility…
Symmetry-protected topological phases of matter have challenged our understanding of condensed matter systems and harbour exotic phenomena promising to address major technological challenges. Considerable understanding of these phases of…