At first one might not believe that nanotechnology is relevant to jet engines. But actually it is. The smallest size that an aircraft can be is controlled by the thrust to weight ratio of it's engine. Experimental aircraft and ultralight aircraft are all critically sized by the wing area that is necessary to lift, not only the occupant, but the powerplant. Some back-of-the-envelope calculation shows that the jet engine, necessary to loft a single person in a suitable aerodynamic configuration, only needs to weight about 4 pounds. You could hold it in one hand. It would be nine inches long, and three inches wide, about the size of a spray paint can. That is for an engine that would propel a single occupant vehicle. Now go to the next step, what about a jet engine that would propel a small aircraft, not a model in the traditional sense, but perhaps a delivery vehicle for food or goods, with a payload of around a couple of pounds. This would require yet another 100 fold reduction in thrust. There is no reason to stop there. Small jet powered insects could be very useful, carrying video cameras into difficult to reach places rapidly, transmitting messages, etc.. The implications of smallness start piling up pretty quickly. Here is where the "nano" comes in. It is very difficult to build a milli, micro, or nanojet engine without leaving something important out; The typical axial flow turbofan engine can have upwards of 1000 blades in 14 stages of compressor and 2 stages of turbine. Turbine blades are not the smallest part of such an engine. A full sized typical jet engine weighing two tons has very small screws and fasteners that hold together pneumatic, hydraulic and servo electronic control systems that regulate fuel, oil and temperature. The compressor blades in the final stages are around the size of your fingernail and that is for a full size engine. An important question concerns the scaling laws that affect shrinking Brayton cycle devices. What factors dominate as size decreases? Speed of sound? Viscosity? Perhaps there is some minimum dimension beyond which the engine ceases to function. Some new thinking is required to scale a jet engine to the size that it can be held in one hand. Some even newer thinking is required to go two orders of magnitude smaller. Some new thinking is required to build a nanojet engine that can be manufactured cheaply and efficiently. I believe there is a large market for engines at any of those scales. Not just for single occupant applications (microJet), but also for unmanned delivery vehicles used by Fedex, Airborne, Purolator Courier and United Parcel Service. Not to mention the military. Human beings love to employ the latest technology just for killing each other.
There is a saying, "When there is a change of paradigm, everyone goes back to zero." When Texas Instruments first debuted its digital chip for wristwatches in the 1970's they showed it to the Swiss watchmakers. There were 50,000 Swiss watchmakers at the time. None of whom were interested in silicon chips. Now there aren't 500 Swiss watchmakers. Change of paradigm.
Ironically, building a turbine engine this small constitutes a change of paradigm that could reemploy all the watchmakers put out of business by the last one. And enable them to go smaller than they ever dreamed possible.