“…A new degree of freedom, valley, has been introduced into the classical wave systems. The QVHE has been theoretically and experimentally demonstrated in photonic crystals [38][39][40][41]84,85], sonic crystals [42,49,50,53] and mechanical structures [55,[69][70][71][72][73][74][75][76][77][78][79]86,87]. In particular, topologically valley-polarized states in elastic systems have been proposed via bi-layered lattices [69,74], hexagonal lattices [55,70,73,[75][76][77][78][79][88][89][90] and triangular lattices [71,72,86].…”