Title: Coupled metamaterial-phonon terahertz range polaritons in a topological insulator

Abstract: We report terahertz time-domain spectroscopy (TDTS) experiments demonstrating strong light-matter coupling in a terahertz (THz) LC-metamaterial in which the phonon resonance of a topological insulator (TI) thin film is coupled to the photonic modes of an array of electronic split-ring resonators. As we tune the metamaterial resonance frequency through the frequency of the low frequency $\alpha$ mode of (Bi$_x$Sb$_{1-x}$)$_2$Te$_3$ (BST), we observe strong mixing and level repulsion between phonon and metamaterial resonance. This hybrid resonance is a phonon polariton. We observe a normalized coupling strength, $\eta$ = $\Omega_R$/$\omega_c$ $\approx$ 0.09, using the measured vacuum Rabi frequency and cavity resonance. Our results demonstrate that one can tune the mechanical properties of materials by changing their electromagnetic environment and therefore modify their magnetic and topological degrees of freedom via coupling to the lattice in this fashion.