Why does a field-effect transistor (FET) with wrap-around gate work at all? In the recent years several publications have presented field-effect transistors (FETs) that are based on semiconductor nanowires with a gate electrode that is wrapped around the whole nanowire circumference (e.g. [1], [2]) where it is said that this wrap-around or all-around gate configuration gives the best control to deplete the charge carriers from the region within the gate.
However, this somewhat contradicts to typical textbook electrostatics: according to Gauss' Law the electric field within a charged cylinder shell is zero, which is the reason why coaxial and shielded cables work – an electric charge that is somehow induced at the shield conductor does not affect the signal line that are within the shield. If one now makes the naive assumption that the wrap-around gate is basically a piece of cylinder shell wrapped around the semiconductor material, I would expect that whatever voltage is applied to it should not cause an electric field on its inside and hence not cause a carrier depletion. So from this point of view this transistor design should not work at all, not to mention better than other designs.
So the question is which of my assumptions is wrong in this context and how is it to be fixed to make this whole thing work?
 A: The electric field within a charged cylinder shell is NOT zero when you have a coaxial conductor inside that is held at a different potential than the outer shell. This is already the case in a cylindrical capacitor with coaxial metal electrodes. If in such a coaxial cylindrical capacitor (with an insulator filling the space between the electrodes), you replace the inner metal with a semiconductor and attach ohmic contacts to both ends of the semiconducting cylinder then you already have, in principle, a wrap-around gate metal-insulator-semiconductor field-effect-transistor (MISFET). In this an applied voltage between the outer metal (gate) and the inner semiconductor creates an electric field inducing a charge on the inner semiconductor producing a conducting inversion channel that can be controlled by the applied gate voltage between the outer metal and the inner semiconductor (usually one contact called source). This can be used to modulate the current produced by an applied voltage (drain-source voltage) between the contacts at the ends of the inner semiconductor which is then a wrap-around gate MISFET or MOSFET when the insulator is an oxide.        
