Tunneling current induced phonon generation in nanostructures

We analyze generation of phonons in tunneling structures with two electron states coupled by electron-phonon interaction. The conditions of strong vibration excitations are determined and dependence of non-equilibrium phonon occupation numbers on the applied bias is found. For high vibration excitation levels self consistent theory for the tunneling transport is presented. Tunneling current induces generation of phonons (or vibrational quanta for a molecule) leading to effective ”heating” of the phonon subsystem in any real system with electron-phonon interaction. In scanning tunneling microscopy experiments this effect may induce motion, dissociation or desorption of adsorbed molecules thus allows single molecule manipulation on a surface [1],[2], [3]. The main purpose of the present work is to reveal the conditions for strong phonon generation as well as for its suppression. We also investigate the influence of strong phonon generation on tunneling conductivity behavior. In our previous work [4] we analyzed modifications of the tunneling current using a model in which electron-phonon interaction leads to transitions between two electron levels. In the present paper we demonstrate that in this system tunneling current can induce strong phonon generation. The mechanism of this enhanced phonon heating is closely connected with the presence of at least two electron states in a molecule or a quantum dot, and in a single level model, widely discussed in literature ([5],[6],[7]), this mechanism is absent. We consider a tunneling system, which is described by the Hamiltonian of the following type: Ĥ = Ĥdot + Ĥtun + Ĥ0 (1) The part Ĥdot corresponds to a QD or a molecule with two localized states taking into account. Electronphonon interaction leads to transitions between these two states. Ĥdot = ∑ i=1,2 εia + i ai + g(a + 1 a2 + a + 2 a1)(b+ b ) + ω0b b (2) where εi corresponds to discrete levels in quantum dot (or two electron states in molecule) and we adopt that ε1 > ε2 , ω0 — optical phonon frequency (or molecule vibrational mode)and g — is electron-phonon coupling constant. Tunneling transitions from the intermediate system are included in Ĥtun Ĥtun = ∑ p,i=1,2 Tp,i(c + pai + h.c.) + ∑ k,i=1,2 Tk,i(c + k ai + h.c.) (3) And free electron spectrum in left and right electrodes (k and p) includes the applied bias V : Ĥ0 = ∑ k (εk − μ)c + k ck + ∑ p (εp − μ− eV )c + p cp (4) ∗e-mail: [email protected]