Dynamical electron transport through a nanoelectromechanical wire in a magnetic field

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We investigate dynamical transport properties of interacting electrons moving in a vibrating nanoelectromechanical wire in a magnetic field. We have built an exactly solvable model in which electric current and mechanical oscillation are treated fully quantum mechanically on an equal footing. Quantum mechanically fluctuating Aharonov-Bohm phases obtained by the electrons cause nontrivial contribution to mechanical vibration and electrical conduction of the wire. We demonstrate our theory by calculating the admittance of the wire which are influenced by the multiple interplay between the mechanical and the electrical energy scales, magnetic field strength, and the electron-electron interaction.