Acoustic non-Hermitian skin effect from twisted winding topology

Li Zhang,Shou-Qi Yuan,Hongsheng Chen,Baile Zhang,Ding Jia,Hong-Xiang Sun,Qiaolu Chen,Qinghui Yan,Rui Xi,Yong Ge,Yi-Jun Guan,Fujia Chen,Yuanzhen Li,Yihao Yang

doi:10.1038/s41467-021-26619-8

Abstract

The recently discovered non-Hermitian skin effect (NHSE) manifests the breakdown of current classification of topological phases in energy-nonconservative systems, and necessitates the introduction of non-Hermitian band topology. So far, all NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop. As recently characterized along a synthetic dimension on a photonic platform, non-Hermitian band topology can exhibit almost arbitrary windings in momentum space, but their actual phenomena in real physical systems remain unclear. Here, we report the experimental realization of NHSE in a one-dimensional (1D) non-reciprocal acoustic crystal. With direct acoustic measurement, we demonstrate that a twisted winding, whose topology consists of two oppositely oriented loops in contact rather than a single loop, will dramatically change the NHSE, following previous predictions of unique features such as the bipolar localization and the Bloch point for a Bloch-wave-like extended state. This work reveals previously unnoticed features of NHSE, and provides the observation of physical phenomena originating from complex non-Hermitian winding topology.

Highlights

The recently discovered non-Hermitian skin effect (NHSE) manifests the breakdown of current classification of topological phases in energy-nonconservative systems, and necessitates the introduction of non-Hermitian band topology
The complete collapse of bulk bands in NHSE has posed a challenge to the bulk-boundary correspondence3—a fundamental principle of topological physics—which states that the band topology derived from the bulk dictates the topological phenomena at the boundary
All NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop in the complex plane[7–9,15]

Summary

Results

Two identical acoustic resonators (labeled “1” and “2”) with resonance frequency ω0 are connected by two narrow waveguides that provide reciprocal coupling κ1 (see Supplementary Information Note 2). The two resonance frequencies are different from those in the Hermitian case, indicating that the non-reciprocal coupling has changed the eigenfrequencies of the system. By numerically fitting the measured spectra with the coupled-mode theory (see Supplementary Information Note 4), we can obtain the resonator’s resonance frequency ω0 = 1706 Hz, the reciprocal coupling κ1 = 24 Hz, the non-reciprocal coupling ~κa = −11 + 3.9i Hz, and γ0 = 2.13 Hz, respectively. The non-reciprocal coupling is applied between nearest-neighbor resonators, following the tight-binding model in Fig. 3b (see Methods for more details).

Discussion

Methods

Code availability