相关论文: Topological D-Class Physics with Passive Acoustic …

Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological…

Topological superconductors are a class of unconventional superconducting materials featuring sub-gap zero-energy Majorana bound modes that hold promise as a building block for topological quantum computing. In this work, we study the…

For D-dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D- or (D+1)-dimensional integration over a certain curvature function that is expressed in terms of…

Topological phononic crystals (PCs) are periodic artificial structures which can support nontrivial acoustic topological bands, and their topological properties are linked to the existence of topological edge modes. Most previous studies…

Recently, the higher-order topological phases from the chiral AIII symmetry classes are characterized by a Z topological invariant known as the multipole chiral numbers, which indicate the number of degenerate zero-energy corner states at…

Topological crystalline insulators define a new class of topological insulator phases with gapless surface states protected by crystalline symmetries. In this work, we present a general theory to classify topological crystalline insulator…

Recently, the theory of quantized dipole polarization has been extended to account for electric multipole moments, giving rise to the discovery of multipole topological insulators (TIs). Both two-dimensional (2D) quadrupole and…

Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy…

The research in topological materials and meta-materials reached maturity and is now gradually entering the phase of practical applications and devices. However, scaling down the experimental demonstrations definitely presents a challenge.…

Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After…

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a…

We systematically study topological phases of insulators and superconductors (SCs) in 3D. We find that there exist 3D topologically non-trivial insulators or SCs in 5 out of 10 symmetry classes introduced by Altland and Zirnbauer within the…

High-order topological insulators (TIs) are a family of recently-predicted topological phases of matter obeying an extended topological bulk-boundary correspondence principle. For example, a two-dimensional (2D) second-order TI does not…

Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to…

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…

Topological interface states (TISs) in phononic crystals (PnCs) are robust acoustic modes against external perturbations, which are of great significance in scientific and engineering communities. However, designing a pair of PnCs with…

Topological insulators, which allow edge or interface waves but forbid bulk waves, have revolutionized our scientific cognition of acoustic/elastic systems. Due to their nontrivial topological characteristics, edge (interface)waves are…

We present a framework for characterizing higher-order topological phases directly from the one-particle density matrix, without any reference to an underlying Hamiltonian. Our approach extends the mode-shell correspondence, originally…

Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the…

Recent attempts at topological materials have revealed a large class of materials that show gapless surface states protected by time-reversal symmetry and crystal symmetries. Among them, topological insulating states protected by crystal…