It’s actually hard to say. I’ll have a go; take it with a grain of salt:
Solar Energy : Now-a-days, physics or material science because the breakthroughs are (presumably) better photo-voltaics. Otherwise mechanical engineering because it’s positioning control. (This used to be a Mech-Eng topic when people were interested in solar bonds and so on.)
-Rocket Propulsion: If your interest in propulsion, that’s gas dynamics. Mechanical engineering. There are other topics in rocketry, but propulsion is ME.
-Nuclear Fusion/Plasma Physics: Nuclear engineering.
-Astrophysics: Physics
-Nanotechnology: Probably, physics, chemistry, material science, chemical engineering. (The people I know working in nanotechnology are chemical engineers. That doesn’t mean others don’t also.)
-Electric Vehicles: Battery technology is chemistry. Vehicle dynamics is mechanical engineering.
-Remanufacturing/Making the transition to circular economy: I don’t even know what this is. So take this with a huge block of salt: Industrial engineering.
-Artificial Intelligence: Computer science/math.
-Biotechnology/Engineering Living Matter: Look for bio engineering. Otherwise: could be anything.
-Wind/Hydropower: Mechanical engineering.