This is very interesting - however, it's not a totally new technology, just a small incremental improvement over spectrolab's shipping products (which get around 36%).
Unlike 'normal' silicon PV, this material is designed for optical concentrators. This is advantageous because only a small area of the very expensive PV is required (only 1 cm^2 of PV is required for each 30W of electrical output), but it complicates the design by requring a focused concentrator, a precise 2-axis sun-tracking mechanism, and some form of active cooling (water cooling, or a massive heatsink) for the PV.
You also don't fully utilise the improved efficiency due to inefficiency in the concentrator and the inability to focus diffuse light (this is a killer in areas which receive a lot of haze, or thin cloud cover).
The other potential disadvantage is that the semiconductor contains gallium arsenide - which isn't particularly environmentally friendly.