Abstract
Weyl points (WPs), nodal degenerate points in three-dimensional (3D) momentum space, are said to be ‘ideal’ if they are symmetry-related and well-separated, and reside at the same energy and far from nontopological bands. Although type-II WPs have unique spectral characteristics compared with type-I counterparts, ideal type-II WPs have not yet been reported due to the lack of an experimental platform with enough flexibility to produce strongly tilted dispersion bands. Here we experimentally realize a topological circuit that hosts only topological bands with a minimal number of four ideal type-II WPs. By stacking two-dimensional (2D) layers of inductor-capacitor (LC) resonator dimers with the broken parity inversion symmetry (P), we achieve a strongly tilted band structure with two group velocities in the same direction, and topological surface states in an incomplete bandgap. Our results establish an ideal system for the further study of Weyl physics and other exotic topological phenomena.
On the quasistatic effective elastic moduli for elastic waves in three-dimensional phononic crystals
