Any design similar to or
Any design similar to or based on a propeller quickly drops in effectiveness as you approach Mach 1.
There are a bunch of electric propulsion ideas that work completely without moving parts and thus work well at supersonic speeds. The most notable ones are probably:
1. arc-jets (You generate lightning inside your propulsion chamber to head up and expand air)
2. magneto-plasma-dynamic thrusters (You once again generate a lightning arc, but then you use a powerful magnetic field to deflect the ions towards the rear to produce thrust)
Both of theses are heavily in science fiction territory though since in order to work at acceptable efficiency they require the air to be way more conductive than it normally is.
One article I read on the subject proposed using a combination of burning caesium and micro waves in order to ionize the air inside the thruster which might work, but is pretty expensive and energy consuming on it's own...