Topological mechanical metamaterials translate condensed matter phenomena, like non-reciprocity and robustness to defects, into classical platforms 1,2 . At small scales, topological nanoelectromechanical metamaterials (NEMM) can enable the realization of on-chip acoustic components, like unidirectional waveguides and compact delay-lines for mobile devices. Here, we report the experimental realization of NEMM phononic topological insulators, consisting of two-dimensional arrays of free-standing silicon nitride (SiN) nanomembranes that operate at high frequencies (10-20 MHz). We experimentally demonstrate the presence of edge states, by characterizing their localization and Dirac cone-like frequency dispersion. Our topological waveguides also exhibit robustness to waveguide distortions and
Nanoelectromechanical systems (NEMS) 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. NEMS platforms with single- or low-degrees of freedom have been employed to demonstrate quantum-like effects, such as mode cooling, mechanically induced transparency, Rabi oscillation, two-mode squeezing and phonon lasing. Periodic arrays of NEMS resonators with architected unit cells enable fundamental studies of lattice-based solid-state phenomena, such as bandgaps, energy transport, non-linear dynamics and localization, and topological properties, 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 NEMS-based phonon waveguides and includes the voltage-induced frequency tuning of the individual resonators. 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. 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.
In this work, methods for the efficient simulation of large systems embedded in a molecular environment are presented. These methods combine linear-scaling (LS) Kohn-Sham (KS) density functional theory (DFT) with subsystem (SS) DFT. LS DFT is efficient for large subsystems, while SS DFT is linear scaling with a smaller prefactor for large sets of small molecules. The combination of SS and LS, which is an embedding approach, can result in a 10-fold speedup over a pure LS simulation for large systems in aqueous solution. In addition to a ground-state Born-Oppenheimer SS+LS implementation, a time-dependent density functional theory-based Ehrenfest molecular dynamics (EMD) using density matrix propagation is presented that allows for performing nonadiabatic dynamics. Density matrix-based EMD in the SS framework is naturally linear scaling and appears suitable to study the electronic dynamics of molecules in solution. In the LS framework, linear scaling results as long as the density matrix remains sparse during time propagation. However, we generally find a less than exponential decay of the density matrix after a sufficiently long EMD run, preventing LS EMD simulations with arbitrary accuracy. The methods are tested on various systems, including spectroscopy on dyes, the electronic structure of TiO2 nanoparticles, electronic transport in carbon nanotubes, and the satellite tobacco mosaic virus in explicit solution.
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