Orbital degree of freedom induced multiple sets of second-order topological states in two-dimensional breathing Kagome crystals

Abstract

The lattice geometry induced second-order topological corner states in breathing Kagome lattice have attracted enormous research interests, while the realistic breathing Kagome materials identified as second-order topological insulators are still lacking. Here, we report by first-principles calculations the second-order topological states emerging in two-dimensional d-orbital breathing Kagome crystals, i.e., monolayer niobium/tantalum chalcogenide halides M3QX7 (M = Nb, Ta; Q = S, Se, Te; X = Cl, Br, I). We find that the orbital degree of freedom of d orbitals can give rise to multiple sets of corner states. Combining fraction corner anomaly, orbital components and real space distribution of the corner states, we can also identify the topology of these corner states. Our work not only extends the lattice geometry induced second-order topological states to realistic materials, but also builds a clear and complete picture on their multiple sets of second-order topological states.

Disentangled Higher‐Orbital Bands and Chiral Symmetric Topology in Confined Mie Resonance Photonic Crystals

“…These different-order orbital band structures are critical for many significant physical phenomena, such as the existence of Majorana bound states in pwave superconductors, [32] the higher-temperature superconducting phases in d-wave superconductors [33] and multiple sets of corner states induced by the d-orbital bands. [34] Most studies on photonic crystals have focused on the s-wave band structure, [35] and there have been a few examples studying the higher-orbital bands structure, which have shown intriguing physical effects. For instance, negative coupling can be realized in a photonic waveguide array with both s-and p-orbitals and that octupole insulators can be observed in d-wave photonic bands.…”

Atomic-Limit Mott Insulator in [4]Triangulene Frameworks

“…One group is sitting at the Fermi level (labeled as I) and the other group is sitting below the valence edge states (labeled as II), which are spatially localized at six corner regions (inset of Figure d). Although the 2D SOTIs have been studied in various solid-state materials − and artificial systems, so far, the theoretically proposed − and experimentally confirmed − topological corner states are mainly limited in the cluster configuration. Due to the special geometry structure, we found that the topological corner states of [4]-TGF not only exist in the cluster but also exist in the anticluster configuration.…”

Pseudospin Polarized Dual-Higher-Order Topology in Hydrogen-Substituted Graphdiyne

“…Recently, the higher-order topological band theory was established, − in which the nontrivial topology of an m -dimensional n th-order TI is characterized by gapless states at the ( m–n )-dimensional boundary and gapped states otherwise. , Different to the conventional TIs, the higher-order nontrivial gap is not induced by SOC. − This indicates that the higher-order Fermionic and bosonic topological phases will be compatible with each other, which can be created by the same mechanism without SOC, achieving the so-called dual-higher-order topology in one material.…”