Phonon circular birefringence and polarization-filter in Magnetic Topological Insulators

Abstract

The surface phonon Hall viscosity (PHV)-an acoustic analog of axion electrodynamics-emerges from the strain response of magnetic topological insulators and gives rise to novel acoustic phenomena. In this work, we propose a previously unexplored effect: a phonon polarization-filter mechanism induced by the surface PHV, which generates an interface phonon mode with its frequency below the bulk mode frequency. This interface mode possesses a specific circular polarization and therefore acts as a polarization filter, confining only phonons with the matching polarization at the interface. Magnetic topological insulators can thus selectively transmit one type of circularly polarized phonon mode, enabling the manipulation of phonon polarization and angular momentum. In addition, we further develop a generalized scattering framework to study the effect of an injected acoustic wave from a trivial insulator to a magnetic topological insulator with both normal and oblique incidence, and discuss the phenomena of surface acoustic Faraday rotation and longitudinal-transverse mode conversion. Our results establish surface Hall viscosity as a powerful mechanism for engineering axial phonon states and open new avenues for topological phononic devices based on phonon angular momentum.

Figures (5)

• Figure 1: (a) The schematic of the proposed phonon polarization-filter based on the interface of magnetic TI structure. Injecting a linearly polarized wave leads to the detection of either a RCP or LCP wave near the interface, depending on the interface magnetization. (b) Schematic of the surface scattering phenomena - acoustic Faraday rotation and the (c) longitudinal-transverse mode conversion. The blue and black arrows depict the propagation and polarization directions, respectively.
• Figure 2: (a) The setup of the phonon polarization-filter, where the injected wave at $y=0$ is linearly polarized along the $x$-direction and the transmitted wave detected at $y=W$ is either RCP or LCP. (b) The phonon frequency in the isotropic approximation. The interface phonon mode is depicted in green and the bulk modes are in blue. (c) The $z$-profile of the interface mode at $k_y = 4$ nm$^{-1}$. We use $c_t = 1500, c_l = 2500$ in units of m/s and $\eta_1 = 0.16 \eta_0, \eta_2 = 0.11 \eta_0, \eta_3 = 0.07 \eta_0$ where $\eta_0$ is in units of $\frac{1}{\rho_0} \frac{1}{\hbar} \frac{1}{(\mu m)^2}$
• Figure 3: (a) The phonon angular momentum $L_y$ in the $xz$-plane for the interface eigen-mode as a function of the surface PHV coefficient $\eta_0$. (b) The phonon angular momentum $\Tilde{L}_y^t(z)$ as a function of $z$ for the interface mode with $\eta_0 > 0$ (in green) and $\eta_0 < 0$ (in red). The $\Tilde{L}_y^t(z)$ due to a sum over all the contributing modes for $\eta_0 > 0$ (in black) and $\eta_0<0$ (in blue). Here, we use an injected wave frequency $\omega = 2.5$ meV. (c) The phonon angular momentum $L_y^t$ in the $xz$-plane for the transmitted mode near the interface as a function of the surface PHV coefficient $\eta_0$. We separate the contributions from the interface mode (in green) and all the propagating modes (in black). We use $c_t = 1500, c_l = 2500$ in units of m/s and $\eta_1 = 0.16 \eta_0, \eta_2 = 0.11 \eta_0, \eta_3 = 0.07 \eta_0$ where $\eta_0$ is in units of $\frac{1}{\rho_0} \frac{1}{\hbar} \frac{1}{(\mu m)^2}$.
• Figure 4: (a) The setup of the acoustic Faraday effect due to the surface phonon Hall viscosity. The blue arrows depict the direction of propagation and the black arrows depict the polarization. (b) The acoustic Faraday angle $\tan \Phi_F$ as a function of the injected elastic wave frequency $\omega$ for different $\eta_2$. $\eta_2$ is in units of $\frac{1}{\rho_0} \frac{1}{\hbar} \frac{1}{(\mu m)^2}$.
• Figure 5: (a) The setup for the longitudinal-transverse mode conversion. The blue arrows depict the direction of propagation and the black arrows depict the polarization. The green arrows for $u_{LT_{1,2}}^t$ depicts the projection of the polarization $u_0^t$ on the $LT_{1,2}$ planes. The angles made by $u_{LT_{1,2}}$ with the $L$ axis are $\theta_{T_{1,2}}$ (b) The conversion efficiency characterized by angles $\theta_{T_1}, \theta_{T_2}$ along the two transverse directions as a function of $\omega$ for different $\eta_0$. We use $\eta_{1,3}$ in units of $\frac{1}{\rho_0} \frac{1}{\hbar} \frac{1}{(\mu m)^2}$ and $c_t = 3500$ m/s, $k_z = 0.03$ nm$^{-1}$, $\eta_2=0$.