Dynamical electron transport through a nanoelectromechanical wire in a magnetic field

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 the electron-electron interaction is considered nonperturbatively and the electric current and mechanical vibration are treated fully quantum mechanically on an equal footing. We demonstrate our theory by calculating the admittance of a finite-size wire, which is influenced by the magnetic field strength, the electron-electron interaction, and the complex interplay between the mechanical and the electrical energy scales. Nontrivial features including sharp resonance peaks appear in the admittance, which may be experimentally observable.