Fig. 2: Manifestation of deterministic Dirac degeneracy and degenerated states.
From: Robust separation of topological in-plane and out-of-plane waves in a phononic crystal
a Three conditions [(I), (II), and (III)] and associated schematics of primitive cells individually guaranteeing the deterministic Dirac degeneracy at K or K′ for the phononic crystals (PCs). b Parameters (solid violet lines) of the PCs satisfying conditions (I), (II), or (III), or equivalently, having deterministic Dirac degeneracy at K or K′ in the restricted parameter space (volume enclosed by gray solid lines). PDD indicates the set of all such parameters. The complete parameter space is described in Supplementary Note 1. c Energy distributions and displacement fields of a primitive cell of the PC with parameter (0, 0, 0) at the in-plane polarized (IPP) and out-of-plane polarized (OPP) Dirac degeneracies at K point. Arrows on the energy distribution, blue for IPP, and red for OPP wave show the rotation direction of the motion. Four displacement fields taken at one-third of a period interval show the time-varying motion of the degenerated state; top view presents for IPP states and perspective view presents present for OPP states, and black arrow in OPP displacement field points to the displacement maxima. The black circle and arrow associated with each displacement field show the direction of the motion as well as the phase step. Characters (p− or q+) and triangular symbols are a shorthand representation of the state; moving sublattices (location of moving sublattices) and signs (fill) indicating the rotation direction are used for characters (symbols), and colored blue for IPP and red for OPP state.
