Mechanical Stabilization of Nanoscale Conductors by Plasmon Oscillations

External driving of the Fermion reservoirs interacting with a nanoscale charge-conductor is shown to enhance its mechanical stability during resonant tunneling. This counterintuitive cooling effect is predicted despite the net energy flow into the device. Field-induced plasmon oscillations stir the energy distribution of charge carriers near the reservoir’s chemical potentials into a nonequilibrium state with favored transport of low-energy electrons. Consequently, excess heating of mechanical degrees of freedom in the conductor is suppressed. We demonstrate and analyze this effect for a generic model of mechanical instability in nanoelectronic devices, covering a broad range of parameters. Plasmon-induced stabilization is suggested as a feasible strategy to confront a major problem of current-induced heating and breakdown of nanoscale systems operating far from equilibrium.


ˆˆˆˆˆĤ H H H [H ( ) H ( ) h .c.]
M R L MR ML tt = + + + + + . (S1) The time-dependent molecule-leads couplings read (for , where, for time-periodic coupling, with a period, 2 T   = , one has, The second term in the right hand side accounts for the molecule lead interactions. Using the explicit form of the coupling operators, , and the product form of the zero order propagator, 0 ( , ') (S6) can be rewritten as, The molecular space operators, () () and the lead correlation functions are, † †ˆ( For the analysis of steady-state molecular observables in the weak molecule-leads coupling limit, it is instructive to study Eq.(S7) in the basis of the molecular eigenstates, defined by, Focusing on the eigenstate populations dynamics, and neglecting the coupling to coherences, when the molecule-lead coupling energy is much smaller than the energy gaps between the molecular eigenstates, Eq. (S7) yields, Eq. (S10) is rewritten as a quantum master equation, Using the Fourier expansion of the periodic molecule-lead interaction, Eq. (S3), one obtains, (S13)

B. The wide band limit
We now consider explicitly the non-interacting lead Hamiltonians ( , K L R  ), and the molecule-lead coupling operators (in the lead space), defined as, †Ĥ (S14) † K k b is the electron creation operator in the single particle state at the K th lead, K k  is the corresponding lead orbital energy, and K k  is the respective molecule-lead coupling parameter.
For this model, the lead correlation functions (Eq. (S9)) take the explicit forms, where, . For a dense electrode spectrum, the summation can be replaced by an integral over the lead spectral density, (S16) The wide-band limit assumes that the electrode band is sufficiently wide, and that () the upper limit of the time integrals in Eq. (S16) can be taken to infinity with a negligible effect on the result. The wide band limit of the transfer rates therefore reads,

C. Time-averaged rates
Owing to the explicit driving field oscillations associated with the terms { ( ') , remain time-dependent even when wide band limit can be applied. However, in many cases of interest, the time-period of the driving field is much 7 shorter than the typical times for population transfer between the system eigenstates. In such cases, it is instructive to replace the transient rates in the master equation (Eq. (S12)) with their time average over the driving field period. The rate equations become, with the averaged rates defined as, which holds when the field frequency is larger than the transfer rate for any n and k , where we identify, The eigenstates of the molecular Hamiltonians, Eq. (S28), are products, where 01  are Franck Condon overlap integrals between displaced harmonic vibrational eigenfunctions associated with the two charging states of the molecule.
We now notice that the basic requirements for invoking the wide band approximation are fulfilled for the present model. In particular, the FC integrals decay to zero for arbitrarily large differences between the vibrational quantum numbers 0  , and 1  , such that Eq. (S18) is satisfied. Additionally, expanding the driving function in Eq. (S29) as Fourier series, one obtains,

E. The non-equilibrium vibrational temperature
Restricting again to the weak vibronic coupling limit as discussed above, the nonvanishing electronic transition rates are associated with an exchange of up to a single vibration quantum (Eq. (S35)). Using this result in the time-averaged quantum master equations (Eq. (S22)), otain the following compact form, where, where  is a the non-equilibrium inverse vibrational temperature.