Excitation gap of a nano-electromechanical rod in magnetic fields

Using an exactly solvable model, we investigate quantum transport properties of electrons in a nano-electromechanical rod of finite thickness at magnetic fields. The electronʹs motion is coupled to the rodʹs mechanical displacement through its magnetic gauge potential. We obtain two bosonic modes and find one of the bosonic modes has the excitation gap View the MathML source which was previously introduced for a nano-electromechanical string [K.-H. Ahn, H. Yi, Europhys. Lett. 67 (641) (2004)]. In contrast to the case of nano-strings, the dispersion relation of the eigenmodes has (avoided-) level crossing point at a large wave number. We demonstrate our theory by calculating the current response to an oscillating external electric field which clearly shows a resonance behavior at ωB.