What is the best university to approach with a reasearch idea involving theoretical solar technology?

M.I.T.?

Yeah, M.I.T. unless you can’t afford it or can’t get in

UC Berkeley would be my choice.

Here is a professor researching it at University of Califronia Merced.

Here is a link to a Fox News story announcing the establishment of a new Solar Power Laboratory this year at Arizona State University.

This article details solar panel research going on at the University of Delaware.

Caltech, which emphasizes natural sciences and engineering, would be an excellent choice, although those previously mentioned, are all very good