Putting Quantum Into Mechanics

Theoretical Investigation of Nano-Electro-Mechanical Systems

This report details a theoretical investigation of the time-independent, finite temperature, behaviours of Nano-Electro-Mechanical Systems. Based on prior zero-temperature work [M. Tahir. (2010). Quantum Behaviour in Nano-Mechanical Systems. PhD thesis, ICL.]. Non-equilibrium Green’s function methods were used to model a single site quantum dot in the Coulomb blockage regime, coupled via tunnel junctions to two metallic leads in the wide-band limit. The model was developed to include a quantum harmonic oscillator strongly coupled to the dot. Both electronic and mechanical degrees of freedom were treated quantum mechanically. Finite temperature was incorporated by breaking down the associated Fermi function into a sum over Matsubara poles.
Analytic solutions were found for current through the dot and the density matrix of the dot-oscillator sub-system, recovering prior results in the zero-temperature limit. The system was found to display a mix of quantum and classical behaviour, with step like features resulting from quantisation, whereas the oscillator was driven into a state resembling classical oscillation. The Seebeck effect was found to be significant when the difference of lead thermal energies was comparable to their difference of Fermi energies. Entanglement was shown within the system’s density matrix and found to have a strong dependence on coupling strength.