Topological sound pumping of zero-dimensional bound states

Abstract: Topological phases have spurred unprecedented abilities for sound, light and matter engineering and recent progress has shown how waves not only confine at the interfaces between topologically distinct insulators, but in the form of zero-dimensional non-propagating states bound to defects or corners. Majorana-like bound states have recently been observed in man-made Kekul\'e textured lattices. We show here how the acoustic version of the associated Jackiw-Rossi vortex embodies a Thouless pumping process, in which the spectral flow of corner states adiabatically merge with the said Majorana-like state. Moreover, we argue how the chirality of the Kekul\'e vortex additionally maps into a 2D quantum-Hall system comprising spatially separated sonic hotspots. We foresee that our findings should provide novel exotic tools to enable contemporary control over sound.