Coupling between vibration and Luttinger liquid in mechanical nanowires

TL;DR

This paper explores how mechanical vibrations in nanowires can couple with electronic Luttinger liquids, revealing a new interaction mechanism that affects conductance and can induce instabilities, with potential applications in nano-mechanical control.

Contribution

It introduces a novel coupling mechanism between nanowire vibrations and Luttinger liquids, including the prediction of vibration instability and conductance oscillations.

Findings

Transverse vibrations cause significant frequency shifts.

Vibration-induced instability occurs at a critical temperature.

Conductance oscillations reveal the Luttinger parameter.

Abstract

The vibration of the mechanical nanowire coupled to photons via photon pressure and coupled to charges via the capacity has been widely explored in experiments in the past decades. This system is electrically neutral, thus its coupling to the other degrees of freedom is always challenging. Here, we show that the vibration can slightly change the nanowire length and the associated Fermi velocity, which leads to coupling between vibration and Luttinger liquid. We consider the transverse and longitudinal vibrations of the nanowires, showing that the transverse vibration is much more significant than the longitudinal vibration, which can be measured through the sizable frequency shift. We predict an instability of the vibration induced by this coupling when the frequency becomes negative at a critical temperature for the transverse vibrations in nanowires with low Fermi energy, which can be reached by tuning the chemical potential and magnetic field. The time-dependent oscillation of the conductance, which directly measures the Luttinger parameter, can provide evidence for this coupling. Our theory offers a new mechanism for exploring the coupling between the vibration and the electronic excitations, which may lead to intriguing applications in cooling and controlling the mechanical oscillators with currents.