Topological sound

Recently, we witnessed a tremendous effort to conquer the realm of acoustics as a possible playground to test with topologically protected sound wave propagation. In this article, we review the latest efforts to explore with sound waves topological states of quantum matter in two- and three-dimensional systems where we discuss how spin and valley degrees of freedom appear as highly novel ingredients to tailor the flow of sound in the form of one-way edge modes and defect-immune protected acoustic waves. Both from a theoretical stand point and based on contemporary experimental verifications, we summarize the latest advancements of the flourishing research frontier on topological sound.X.J.Z. and L.M.H. are supported by the National Natural Science Foundation of China (Grant No. 11625418 and No. 51732006). M.X. is supported by the U. S. National Science Foundation (Grant No. CBET-1641069). Y.C. acknowledges the support from the National Natural Science Foundation of China (NSFC) (Grant Nos. 11834008,11874215, 11674172, and 11574148) and from the National Basic Research Program of China (Grant No. 2017YFA0303702). J.C. acknowledges the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramón y Cajal grant (Grant No. RYC-2015-17156