Why doesn't someone invent a solar roofed commercial jet?

I just read this article about a new Boeing plane.

It claims to be a "green" plane or at least greener than the competitor Airbus plane.

It left me thinking that planes spend much of their life over the clouds. I asked myself, "Do solar panels work when it is cold (e.g. up in the sky)?" Apparently, solar panels work in light and not heat.

I did a quick search on the net and anything related to solar energy and airplanes seems to be trying to make planes fly based solely on solar power. That seems like a big leap. Why not just increase fuel efficiency of real working airplanes by reducing the dependence on fuel for all energy needs. It would be like making a 'hybrid' plane. I wonder how much fuel could be saved if the airplane was using solar energy.

At the very least, maybe those big engines would not have to idle to keep air-conditioning on while waiting on the tarmac for seven hours.