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In this work, we supply an engineering solution that paves the way to theimplementation of the full classification table of topological insulators withpassive acoustic crystals. As an example, we design an acoustic crystaldisplaying the full range of characteristics of a topological insulator fromclass D, such as non-trivial Chern numbers and an exact particle-hole symmetryfor both bulk and edge dynamics. The key is a particular geometry of theacoustic resonators that facilitates a large number of independent andequal-strength couplings, eight to be precise, such that the mode-couplingtheory remains accurate. The latter enables us to implement with high fidelitythe de-complexified tight-binding model generating the topological phases fromclass D in 2-dimensions, previously announced in [Barlas et al, PRB (2018)].The successful realization of a topological acoustic crystal from class D pavesthe way to the observation of the Majorana-like modes stabilized by pi-fluxes.

Topological D-Class Physics with Passive Acoustic Elements