I don't know exactly what the absorption and conversion rates are with the 40% efficient cells, but its safe to say it's very high. One of the biggest hurdles with solar cells is simply getting the charge out, getting the electrons and holes that are knocked out out of the semiconductor. It plays a very large part as to why current efficiencies are so low.
To hit 25+% efficient cells, in essence 3 cells were combined to create a multijunction cell that has 3 layers in series. To get to 30+%, refined deposition methods and clever semiconductor tricks were used. To get to 40+%, you need concentrated light and, in some cells, more layers of different materials.
The journal paper describes a simulated cell with a 14.5% efficiency and that it will compete with crystalline silicon cells - the middle of the pack for silicon efficiency and cost. The big advantage here is that the amount of semiconductor used is very low, which could make these cells very cheap. Another thing to keep in mind is that this method can potentially be applied to other, more efficient technologies, although there will be a few more hurdles should they go that route.
I very much like the idea of cheap solar cells, but it needs to be clear that this is not an efficiency breakthrough. But let me tell you, as a solar car alum, the idea of even a 40+% efficient non-concentrator cell gets me excited, even though this is not that.