Anti-Parity-Time Symmetry in a Su-Schrieffer-Heeger Sonic Lattice

The Su-Schrieffer-Heeger (SSH) model is an important cornerstone in modern condensed-matter topology, yet it is the simplest one-dimensional (1D) tight binding approach to dwell into the characteristics of spinless electrons in chains of staggered bonds. Moreover, the chiral symmetry assures that its surface-confining states pin to zero energy, i.e., they reside midgap in the energy dispersion. Symmetry is also an attribute related to artificial media that are subject to parity P and time-reversal T operations. This non-Hermitian family has been thoroughly nourished in a wave-based context, where anti-PT (APT) symmetric systems are the youngest belonging members, permitting refractionless optics, inverse PT-symmetry breaking transition, and asymmetric mode switching. Here, we report the first extension of APT symmetry in an acoustic setting by endowing a SSH lattice with gain and loss components. We show that the in-gap topological defect state hinges on the non-Hermitian phase, in that the broken symmetry suppresses it, yet when PT or APT symmetry is intact, it is observed with either damped or evanescent decay, respectively. Our experiments showcase how the non-Hermitian SSH lattice serves as a utile platform to investigate topological properties across various PT symmetric phases using sound.