Majorana-like Zero Modes in Kekule Distorted Sonic Lattices

Abstract

[EN] Topological phases have recently been realized in bosonic systems. The associated boundary modes between regions of distinct topology have been used to demonstrate robust waveguiding, protected from defects by the topology of the surrounding bulk. A related type of topologically protected state that is not propagating but is bound to a defect has not been demonstrated to date in a bosonic setting. Here we demonstrate numerically and experimentally that an acoustic mode can be topologically bound to a vortex fabricated in a two-dimensional, Kekul¿e-distorted triangular acoustic lattice. Such lattice realizes an acoustic analog of the Jackiw-Rossi mechanism that topologically binds a bound state in a p-wave superconductor vortex. The acoustic bound state is thus a bosonic analog of a Majorana bound state, where the two valleys replace particle and hole components. We numerically show that it is topologically protected against arbitrary symmetry-preserving local perturbations, and remains pinned to the Dirac frequency of the unperturbed lattice regardless of parameter variations. We demonstrate our prediction experimentally by 3D printing the vortex pattern in a plastic matrix and measuring the spectrum of the acoustic response of the device. Despite viscothermal losses, the measured topological resonance remains robust, with its frequency closely matching our simulations.J. C. acknowledges support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramon y Cajal grant (No. RYC-2015-17156). J. S.-D. acknowledges support from the Ministerio de Economia y Competitividad of the Spanish Government and the European Union "Fondo Europeo de Desarrollo Regional (FEDER)" through Project No. TEC2014-53088-C3-1-R. P. S.-J. acknowledges support from MINECO/FEDER under Grant No. FIS2015-65706-P. D. T. acknowledges financial support through the Ramon y Cajal fellowship under Grant No. RYC-2016-21188 and to the Ministry of Science, Innovation and Universities through Project No. RTI2018-093921-A-C42.Gao, P.; Torrent Martí, D.; Cervera Moreno, FS.; San-Jose, P.; Sánchez-Dehesa Moreno-Cid, J.; Christensen, J. (2019). Majorana-like Zero Modes in Kekule Distorted Sonic Lattices. Physical Review Letters. 123(19):196601-1-196601-4. https://doi.org/10.1103/PhysRevLett.123.196601S196601-1196601-412319Hasan, M. Z., & Kane, C. L. (2010). Colloquium: Topological insulators. Reviews of Modern Physics, 82(4), 3045-3067. doi:10.1103/revmodphys.82.3045Elliott, S. R., & Franz, M. (2015). Colloquium: Majorana fermions in nuclear, particle, and solid-state physics. 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