I recently started my first aquarium. It's a very small 5.5 gallon tank which has been running for a couple weeks now. On the weekend I bought my first fish: two head & tail light tetra and one black neon tetra.

I am very new to the hobby and don't know very much about fish behaviour. It seems to me that one of the head & tail light tetras seems to be dominant over the other two. It tends to eat the most and chases the other two into separate corners of the tank while it occupies the central portion of the tank. The other two swim around a bit but tend to spend a lot of time in opposite and sometimes the same corner of the tank.

Is this common behaviour for tetras? Does anyone have any suggestions or advice?

Ooo... that's a small tank.
Nonetheless, all tetras have different temperaments. In a bigger tank, all tetras will pretty much get along with a few minor scuffles/chases. It's normal.

In your small tank keep an eye out on the fish and make sure they don't cause too much harm to each other.

Head and tail lights are already amoung one of most placid tetras (OK, the neons are the most placid, but H&T tetras aren't far behind.). If you're already facing problems, I suggest you stay clear of Serpae tetras or black widows as they can be more nippy. Also, in a small tank like yours, Tiger barbs would be a BAD idea as well.

Stick with placid fish like neon tetras, cardinal tetras, rummy nose tetras...