Yes, we use leavened bread. Personally, I think an argument for both can be made. The big argument for unleavened bread is that the last supper was during Passover and this is what Christ would have done.
However, Jesus was trying to separate--in a sense--from the Passover since he said "Do this in remembrance [not of Passover but] of me." So, it is certainly possible that he used leavened bread that terrible night.
One explanation I read is that the leaven is the work of the people. To me, leaven is alive and Jesus is alive, although ancients probably didn't see yeast in that way.
Astute question!