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We consider a natural generalization of the lattice model for a periodic array of two layers, A and B, of spinless electrons proposed by Fu [Phys. Rev. Lett. 106, 106802 (2011)] as a prototype for a crystalline insulator. This model has…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…
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…
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…
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…
The electronic properties of interfaces between two different solids can differ strikingly from those of the constituent materials. For instance, metallic conductivity, and even superconductivity, have been recently discovered at interfaces…
Crystalline $\rm Bi_2Se_3$ is one of the most explored three-dimensional topological insulator, with a $0.3\;\rm eV$ energy gap making it promising for applications. Its amorphous counterpart could bring to light new possibilities for large…
We introduce the topological mirror excitonic insulator as a new type of interacting topological crystalline phase in one dimension. Its mirror-symmetry-protected topological properties are driven by exciton physics, and it manifests in the…
Topological phononic states, facilitating acoustic unique transports immunizing to defects and disorders, have significantly revolutionized our scientific cognition of acoustic wave systems. Up to now, the theoretical and experimental…
Crystalline topological insulators have recently become a powerful platform for realizing photonic topological states from microwaves to the visible. Appropriate geometric symmetries of the lattice are at the core of their functionality.…
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this paper, we develop a characterization and classification of…
Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum…
The emergent higher-order topological insulators significantly deepen our understanding of topological physics. Recently, the study has been extended to topological semimetals featuring gapless bulk band nodes. To date, higherorder nodal…
Topological materials (TMs) showcase intriguing physical properties defying expectations based on conventional materials, and hold promise for the development of devices with new functionalities. While several theoretically proposed TMs…
Topological crystalline insulators (TCIs) host topological phases of matter protected by crystal symmetries. Topological surface states in three-dimensional TCIs have been predicted and observed in IV-VI SnTe-class semiconductors. Despite…
The recently-emerged concept of "invisible gateway" with the extraordinary capability to block the waves but allow the passage of other entities has attracted great attentions due to the general interests in illusion devices. However, the…
Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing…
The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface…
We show that certain three-dimensional topological phases can act as acoustic diodes realizing nonlinear odd acoustoelastic effects. Beyond uncovering topologically-induced anomalous acoustic second-harmonic generation and rectification, we…