Abstract
We show that multiple Weyl and double-Weyl points (DWPs) arise in a chiral elastic system through stacking two-dimensional honeycomb mechanical structures. On the distinct kz plane, the band structures calculated from a tight-binding (TB) model exhibit Weyl points (WPs) at Brillouin vertices and DWPs at Brillouin centres. Based on the TB model, a practical chiral mechanical structure can be constructed by 3D printing technology. The numerical calculation illustrates several Weyl and DWPs as expected in our analysis of the TB model. To verify the topological feature, the topological charge of degeneracy is calculated. Within these WPs, we theoretically prove the existence of topologically protected surface modes, and their robustness against defects is also demonstrated.
Highlights
We show that Multiple Weyl and double Weyl points arise in a chiral elastic system through stacking many two-dimensional honeycomb mechanical structures
By mimicking the case of electric field radiated from a charge, Berry curvatures can be regarded as certain fields emitted by a “topological charge” (TC) [1]
Aside from the WPs, several theoretical works indicate that so-called double Weyl points (DWPs), which possess higher topological orders, emerge in the solid-state crystals accompanied by specific symmetries
Summary
We show that Multiple Weyl and double Weyl points arise in a chiral elastic system through stacking many two-dimensional honeycomb mechanical structures. Unlike the single Weyl points (SWPs), which is named to differ from DWPs, the DWP carries TCs whose values are equal to ±2 because DWPs are the coalescence of two SWPs. Generally, in the DWP case, the band crossing is expressed as the quadratic dispersion around the degeneracy in at least one momentum plane, which implies quadratic terms dominates the low-energy Hamiltonian.
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