Topological Acoustic Diode

Abstract

We show that certain three-dimensional topological phases can act as acoustic diodes realizing nonlinear odd acoustoelastic effects. Beyond uncovering topologically-induced anomalous acoustic second-harmonic generation and rectification, we demonstrate how such nonlinear responses are uniquely captured by the momentum-space nonmetricity tensor in the quantum state Hilbert-space geometry. In addition to completing the classification of quantum geometric observables in the quadratic response regime, our findings reveal unexplored avenues for experimental realizations of acoustic diodes using effective $θ$ vacua of axion insulators adaptable for topological engineering applications.

Figures (2)

• Figure 1: Topological acoustic diode responses. (a) Odd acoustic second-harmonic generation. (b) Odd acoustic rectification. The nonlinear acoustic responses to time-dependent distortion fields $w_{ij}(\omega)$ are topologically-induced by the $\theta$-vacuum of an axion insulator ($\theta = \pi$). The acoustoelastic frequency-doubling $J_{zz}(2\omega)$ and rectified $J^\text{dc}_{zz}$ currents flow in the $z$ direction, orthogonally to the mutually perpendicular forcing directions $(x,y)$.
• Figure 2: Nonlinear acoustic responses of an axion insulator diode. (a) Odd second-harmonic response term $\alpha^{2-\text{band}}_{2,xx;yy,zz}$ against the spin-splitting mass term ($m$) controlling the band gap. (b) Odd rectification ($\eta^{\text{odd,rect}}_{xx;yy,zz}$) response of a topological acoustic diode vs. frequencies $\omega$. The real (blue) and imaginary (red) parts of the nonlinear acoustic responses reflect distinct dependences on underlying quantum geometries. In the acoustic second-harmonic susceptibility, the nonmetricity tensor ($N$) contribution dominates the Berry curvature ($\Omega$) term within the total response (Tot.).