Field-induced Gap and Quantized Charge Pumping in Nano-helix

We propose several novel physical phenomena based on nano-scale helical wires. Applying a static electric field transverse to the helical wire induces a metal to insulator transition, with the band gap determined by the applied voltage. Similar idea can be applied to "geometrically" constructing one-dimensional systems with arbitrary external potential. With a quadrupolar electrode configuration, the electric field could rotate in the transverse plane, leading to a quantized dc charge current proportional to the frequency of the rotation. Such a device could be used as a new standard for the high precession measurement of the electric current. The inverse effect implies that passing an electric current through a helical wire in the presence of a transverse static electric field can lead to a mechanical rotation of the helix. This effect can be used to construct nano-scale electro-mechanical motors. Finally, our methodology also enables new ways of controlling and measuring the electronic properties of helical biological molecules such as the DNA.