Can I mount a TV on a single metal stud?
It depends on the mount itself and the size of anchors. Two 1/4 inch lag bolts into a stud can hold hundreds of pounds but if the mount has a long arm the amount of weight is reduced because of the length away from the wall.

The framework may not be able to handle the weight with only one side supported securely. A thick piece of plywood anchored to the stud with lag bolts and fender washers (washers reduce the chance of an over-tightened lag bolt pulling through the plywood) cut to the size of the bracket could carry the load, then attach the monitor frame to the plywood. Using this method, I would use 3/4" plywood and it would be able to handle the load.