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Mass-spring networks (MSNs) have long been used as approximate descriptionsof many biological and engineered systems, from actomyosin networks tomechanical trusses. In the last decade, MSNs have re-attracted theoreticalinterest as models for phononic metamaterials with exotic properties such asnegative Poisson's ratio, negative effective mass, or gapped vibrationalspectra. A practical advantage of MSNs is their tuneability, which allows theinverse design of materials with pre-specified bandgaps. Building on this fact,we demonstrate here that designed MSNs, when subjected to Coriolis forces, canhost topologically protected chiral edge modes at predetermined frequencies,thus enabling robust unidirectional transmission of mechanical waves. Similarto other recently discovered topological materials, the topological phases ofMSNs can be classified by a Chern invariant related to time-reversal symmetrybreaking.

Chiral topological phases in designed mechanical networks