Asking potential PhD supervisors about research
You could do that. However, do keep in mind that asking for something that you could very well do on your own isn't likely to win you any brownie points in their eyes. 

A better option is to find and read several of his/her recent publications. Begin with a Google search, check out their webpage if they have one, search academic databases, etc. Don't email them for papers until you've found and read whatever is easily available. If you find one that is particularly interesting but you can't find the full text anywhere, then is the time to email asking if they'd be willing to share an author copy. 

Familiarize yourself with what they have done. Know what aspects of the past research interests you most. THEN, you will be ready to ask what they are working on now, to have an idea whether you might fit in with their current/ongoing project(s). In this way, you are showing independence, initiative, and responsibilty, all good attributes for a PhD candidate to have.