Two-dimensional higher-order topology in monolayer graphdiyne

Abstract

Based on first-principles calculations and tight-binding model analysis, we propose monolayer graphdiyne as a candidate material for a two-dimensional higher-order topological insulator protected by inversion symmetry. Despite the absence of chiral symmetry, the higher-order topology of monolayer graphdiyne is manifested in the filling anomaly and charge accumulation at two corners. Although its low energy band structure can be properly described by the tight-binding Hamiltonian constructed by using only the p z orbital of each atom, the corresponding bulk band topology is trivial. The nontrivial bulk topology can be correctly captured only when the contribution from the core levels derived from p x,y and s orbitals are included, which is further confirmed by the Wilson loop calculations. We also show that the higher-order band topology of a monolayer graphdyine gives rise to the nontrivial band topology of the corresponding three-dimensional material, ABC-stacked graphdiyne, which hosts monopole nodal lines and hinge states.

From triple-point materials to multiband nodal links

“…3(e) and 3(f) should carry Euler class χ = 2. Note that nodal rings with monopole charges were theoretically related to higher-order topology with hinge Fermi arcs [75][76][77], yet suitable material candidates at present remain very scarce [52]. Our findings suggest that hinge Fermi arcs may arise in spinless triple-point materials; therefore, identifying general conditions for the realization of nontrivial Euler or Stiefel-Whitney monopole charges in TP-materials suggests an interesting future application of our results.…”

“…We expect the nontrivial linking to furnish the NL rings discussed here with monopole charges [49][50][51][52][53][54]. In particular, braiding rules of Ref.…”

“…Curiously, the topological stability of both NLs and TPs is fully captured only if one partitions the energy bands via multiple energy gaps. On the one hand, NLs in spacetime-inversion (PT ) symmetric systems with negligible SOC (i.e., "spinless") exhibit Euler and Stiefel-Whitney monopole charges [49][50][51][52], which are related to linking with NLs inside adjacent energy gaps [53,54]. On the other hand, TPs formed by a crossing of a one-dimensional (1D) and a twodimensional (2D) irreducible corepresentation (ICR) along a rotation axis are end points at which a NL is transferred between two adjacent energy gaps.…”

Transport induced dimer state from topological corner states

“…The existence of one-dimensional hinge states has been experimentally confirmed in bismuth [60] and multi-layer WTe 2 [61]. In 2D higher-order TIs, one-dimensional edges are insulating whereas the cor-ners between different edges can host zero-dimensional ingap states that are isolated from both edge and bulk bands by an energy gap [53][54][55][62][63][64][65]. In contrast to the gapless edge states in conventional topological insulators, higherorder topological corner states are not conducting and behave like localized bound states.…”

Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne

“…It serves as a good starting point for further study of the physics of 3D real topological semimetal phases. We note that some previous works attempted to construct tightbinding models based solely on p z orbitals 62,69 . However, such models fail to capture the correct topology for both 2D and 3D graphdiyne: for 2D, they result in a trivial insulator; for 3D, the obtained k z interval with nontrivial ν R and hinge states is wrong.…”