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Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form…
Different from the traditional bulk-edge correspondence principle, the discovery of higher-order topological states has generated widespread interest. In a second-order, two-dimensional elastic wave topological insulator, the fluctuation…
There are two types of intrinsic surface states in solids. The first type is formed on the surface of topological insulators. Recently, transport of massless Dirac fermions in the band of "topological" states has been demonstrated. States…
We consider the transport properties of topological insulators surface states in the presence of uncorrelated point-like disorder, both in the classical and quantum regimes. The transport properties of those two-dimensional surface states…
Lattice geometry continues providing exotic topological phases in condensed matter physics. Exciting recent examples are the higher-order topological phases, manifesting via localized lower-dimensional boundary states. Moreover, flat…
The seminal Haldane model brings up a paradigm beyond the quantum Hall effect to look for a plethora of topological phases in the honeycomb and other lattices. Here we dwell into this model considering a full parameter space in the presence…
Topological insulators, with metallic boundary states protected against time-reversal-invariant perturbations, are a promising avenue for realizing exotic quantum states of matter including various excitations of collective modes predicted…
A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We…
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…
Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects or local disorder, and can even survive some…
Bound states at sharp corners have been widely viewed as the hallmark of two-dimensional second-order topological insulators and superconductors. In this work, we show that the existence of sublattice degrees of freedom can enrich the…
Higher-order topological insulators (HOTIs) are a novel type of topological phases which supports $d$-dimensional topological boundary states in $D$-dimensional systems with $D-d>1$. In this work, we theoretically predict that interlayer…
Higher-order topological insulators have triggered great interests because of exhibitions of non-trivial bulk topology on lower-dimensional boundaries like corners and hinges. While such interesting phases have been investigated in a…
We present quantum dimer models in two dimensions which realize metallic ground states with Z2 topological order. Our models are generalizations of a dimer model introduced in [PNAS 112,9552-9557 (2015)] to provide an effective description…
We realize an elastic second-order topological insulator hosting both one-dimensional gapped edge states and zero-dimensional in-gap corner modes in the double-sided pillared phononic crystal plates with square lattice. Changing the width…
Inside a three-dimensional strong topological insulator, a tube with $h/2e$ magnetic flux carries a pair of protected one-dimensional linear fermionic modes. This phenomenon is known as the "wormhole effect". In this work, we find that the…
We discuss the possibility of the ``mixed state'' in incommensurate charge density waves with three-dimensional order. It is shown that the mixed state can be created by applying an electric field perpendicular to the chains. This state…
We theoretically investigate a two-dimensional decorated honeycomb lattice framework to realize a second-order topological magnon insulator (SOTMI) phase featuring distinct corner-localized modes. Our study emphasizes the pivotal role of…
Generally, the topological corner state in two-dimensional second-order topological insulator (2D SOTI) is equivalent to the well-known domain wall state, originated from the mass-inversion between two adjacent edges with phase shift of pi.…
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…