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Dynamics of Shuttle Devices

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CHAPTER 2. THE MODELS t exp(-X / )L λ R λt exp(X / ) 1-10 nm QDSource Drain µ L µ R Figure 2.1: Schematic representation of the Single-dot Shuttle: electrons tunnel from the left lead at chemical potential (µL) to the quantum dot and eventually to the right lead at lower chemical potential µR. The position dependent tunneling amplitudes are indicated. X is the displacement from the equilibrium position. The springs represent the harmonic potential in which the central dot can move. the electronic wave functions. The Hamiltonian of the model reads: H = Hsys +Hleads +Hbath +Htun +Hint (2.1) where Hsys = pˆ2 2m + 1 2 mω2xˆ2 + (ε1 − eE xˆ)c†1c1 Hleads = ∑ k (εlkc † lk c lk + εrkc†rkcrk) Htun = ∑ k [Tl(xˆ)c † lk c1 + Tr(xˆ)c†rkc1] + h.c. Hbath +Hint = generic heat bath (2.2) Using the language of quantum optics we call the movable grain alone the system. This is then coupled to two electric baths (the leads) and a generic heat bath. The system is described by a single electronic level of energy ε1 and a harmonic oscillator of mass m and frequency ω. When the dot is charged the electrostatic force (eE) acts on the grain and gives the electrical influence on the mechanical dynamics. The electric field E is generated by the voltage drop between left and right lead. In our model, though, it is kept as an external parameter, also in view of the fact that we will always assume the potential drop to be much larger than any other energy scale of the system (with the only exception of the charging energy of the dot). The operator form xˆ, pˆ for the mechanical variables is due to the quantum treatment of the harmonic oscillator. In terms of creation and annihilation operators for oscillator excitations we would write: 20

Anteprima della Tesi di Andrea Donarini

Anteprima della tesi: Dynamics of Shuttle Devices, Pagina 9

Tesi di Dottorato

Dipartimento: Department if Micro and Nanotechnologies

Autore: Andrea Donarini Contatta »

Composta da 158 pagine.

 

Questa tesi ha raggiunto 319 click dal 01/02/2005.

Disponibile in PDF, la consultazione è esclusivamente in formato digitale.