Electrical tuning of elastic wave propagation in nanomechanical lattices at MHz frequencies

Nanoelectromechanical systems (N EMS) that operate in the megahertz (MHz) regime allow energy transducibility between different physical domains. For example, they convert optical or electrical signals into mechanical motions and vice versa'. This coupling of different physical quantities leads to frequency-tunable NEMS resonators via electromechanical non-linearities(2-4). N EMS platforms with single- or low-degrees of freedom have been employed to demonstrate quantum-like effects, such as mode cooling,, mechanically induced transparencys, Rabi oscillation(6,2), two-mode squeezing, and phonon lasings. Periodic arrays of NEMS resonators with architected unit cells enable fundamental studies of lattice-based solidstate phenomena, such as bandgaps(10,11), energy transporti(0-12), non-linear dynamics and localization's", and topological properties's, directly transferrable to on-chip devices. Here we describe one-dimensional, non-linear, nanoelectromechanical lattices (NEML) with active control of the frequency band dispersion in the radio-frequency domain (10-30 MHz). The design of our systems is inspired by N EMS-based phonon waveguidesim and includes the voltage-induced frequency tuning of the individual resonators(2-4). Our NEMLs consist of a periodic arrangement of mechanically coupled, free-standing nanomembranes with circular clamped boundaries. This design forms a flexural phononic crystal with a well-defined bandgap, 1.8 MHz wide. The application of a d.c. gate voltage creates voltage-dependent on-site potentials, which can significantly shift the frequency bands of the device. Additionally, a dynamic modulation of the voltage triggers non-linear effects, which induce the formation of a phononic bandgap in the acoustic branch, analogous to Peierls transition in condensed matter(16). The gating approach employed here makes the devices more compact than recently proposed systems, whose tunability mostly relies on materials' compliance" and mechanical non-linearities's(19-22).