- Letter
Gigahertz quantum spin Hall effect in nanoelectromechanical phononic crystals
Phys. Rev. Applied 26, L051001 – Published 2 November, 2026
DOI: https://doi.org/10.1103/3gpm-mkyh
Abstract
The quantum spin Hall (QSH) phase is a paradigmatic time-reversal-symmetric topological insulator, carrying a bulk invariant and counterpropagating helical edge channels protected by spin-momentum locking. Since bosonic systems lack the microscopic Kramers degeneracy of electrons, the QSH phase in such systems is engineered from crystalline symmetry to form a synthetic spin-1/2 doublet. This analog has been realized in photonic crystals and in macroscopic kHz-MHz acoustic and elastic structures, but not yet on a chip-scale phononic platform in the microwave regime. The gigahertz (GHz) band is relevant for wireless communications and quantum acoustics, where on-chip work has so far been limited to the valley Hall effect. Here, we report the direct observation of pseudospin-momentum-locked helical phonon edge states at approximately 1 GHz in a nanoelectromechanical aluminum nitride (AlN) topological insulator. An enlarged supercell folds the -point Dirac cones to the point, and tuning the inner-cluster geometry drives a - band inversion with nonzero spin Chern number, in direct correspondence with the Bernevig–Hughes–Zhang Hamiltonian. The helical edge channel along the domain wall is resolved by transmission-mode microwave impedance microscopy. A single--point Fourier filter of the complex displacement field reveals the opposite handedness of the two counterpropagating pseudospin branches. The channel propagates robustly through 120° corners of a Z-shaped waveguide and partitions selectively at a four-domain junction. Together with the valley Hall and Klein-tunneling phenomena already demonstrated on the same platform, our work establishes the acoustic analog of the QSH phase as a building block of an integrated gigahertz phononic toolbox on a CMOS-compatible piezoelectric substrate.