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We present the realization of the topological valley-protected zero-orderantisymmetric (A0) or symmetric (S0) and zero-order shear-horizontal (SH0) Lambwaves at different domain walls based on topologically distinct asymmetricdouble-sided pillared phononic crystals. The elastic periodic structures haveeither the triangular or the honeycomb symmetry and give rise to adouble-negative branch in the dispersion curves. By artificially folding thedoubly negative branch, a degenerate Dirac cone is achieved. Differentpolarization-dependent propagation along the same primary direction along theconstituent branches are presented. Moreover, divergent polarization-dependentphenomena along different primary directions along a given branch are alsoreported. By imposing two large space-inversion symmetry (SIS) breakingperturbations the topological phase transition is obtained. We show that theBerry curvature becomes strongly anisotropic when the wave vector gets awayfrom the valleys. Further, we demonstrate the unidirectional transport of A0,S0, and SH0 Lamb waves at different domain walls in straight or Z-shape waveguides. In the large SIS breaking case, we show negligible reflection at thezigzag outlet of the straight wave guide and occurrence of weak inter-valleyscattering at the bending corners of the Z-shape wave guide. For a largerstrength of SIS breaking, the edge states are gapped and strong reflection atthe zigzag outlet and bending corners is observed. The topological protectioncannot be guaranteed any more in that case.

Polarization-dependent and Valley-protected Lamb Waves in Asymmetric Pillared Phononic Crystals