Contact professors regarding a not registered invention idea
You can always contact professors in order to team up, however it will probably be the case that they will provide PhD students to team up with you. This is just a matter of communication and I don't think that is the real problem here.

The idea not being registered yet raises the real issue, because if you start to emailing everybody to try find a team someone may find the idea interesting and start working on it. Then comes the question is it possible to register the idea like in a patent or something? If not, is it possible to publish a paper about it on a conference, this would be a way to turn the idea public but with an authorship kept.

Another thing related to the team item is that you should first get an adviser and be accepted for a PhD program and then you should worry with the team up for the implementation, maybe even with your adviser help.