Topological insulator and artificial crystals for Hydro-elastic waves

The Quantum Hall effect is the first example of the new topological phases of matter, the state responsible for such effect does not break any symmetries and its explanation comes from topology. The topological phases with non-zero Chern number can lead to interesting wave transport properties such as unidirectional edge propagation immune to back-scattering and robustness against defects/disorder. The study of topological phases has been applied to a variety of classical physical systems, such as photonic [1,2], sonic cristals [3–6] and water waves systems [7,8], each of them presents different challenges to break the time reversal symmetry (T symmetry). Focusing on water wave system it's not trivial to break the T symmetry, in fact rotational water flows are needed comporting a large amount of energy. Another approach to face this experimental challenge is to mimic the Quantum Spin Hall Effect realizing a topological insulator (TI) [9,10], in this case the T symmetry is preserved. We propose to study topological phases using a new approach based on hydro-elastic waves using the spatial symmetry of the unit cell of a triangular lattice in order to construct a pseudo-T symmetry and pseudospin-dependent TI. A band inversion can be achieved by adjusting the lattice's parameters.