Pachysandra, Ivy, Vinca (Myrtle) and Ajuga will all work very well on shady slopes. They are all evergreen.
Ajuga at times can be an aggressive plant. For slopes, this might be a good thing, as you will get fast coverage! Ajuga comes in many different varieties. For example, Bronze Beauty has bronze-like leaves. Other varieties have large leaves, purple foliage, or are variegated. All plants have purple spiked flowers.
Pachysandra produces white flowers in the spring. In addition, it is deer quite deer resistant.
Ivy is a quick grower, and I believe rather aggressive in North Carolina. I know in Virginia it is, and you are further south.
I love Vinca, with its lovely little purple flowers and delicate leaves. This one grows more slowly.
Lily of the Valley and Sweet Woodruff are perennial ground covers. They will disappear after they are finished in the spring. However, they are lovely and you might consider mixing some in.
Consider using many of these suggestions to make a tapestry of plants for a very interesting look.
