Can batteries be recharged by sun exposure?

No, unless you have custom-made rechargeable batteries. It might be possible to build a battery with a built-in solar panel, but it probably wouldn't fit on a "regular" AA battery. It would take a car, or other similarly sized, battery to fit a solar panel. It might also be possible to make a device with that uses solar panels to recharge smaller batteries.

But leaving a regular battery in the sun will not recharge it.