Replying to myself and GP, I found the answers to our questions in the Nature paper linked from the article. The TPV is distinct from a solar cell because the

Replying to myself and GP, I found the answers to our questions in the Nature paper linked from the article. The TPV is distinct from a solar cell because the TPV is meant to reflect energy back to the source. A solar cell also reflects some energy back to the sun, but that energy is effectively lost. In the TPV case, the reflected power helps keeping the source hot, thus effectively recycling photons in a feedback loop involving the source and the TPV. Some of the energy incident to the TPV is transformed into electricity, some is reflected, and some is dissipated as heat in the TPV. The 40% efficiency is measured as (electricity+reflected)/incident. Thus, it is not true that the TPV converts 40% of its input into electricity. Instead, the TPV converts some fraction, reflects (40%-fraction) to be recycled later, and dissipates 60% into heat. Using the TPV as a solar cell would reduce the efficiency because the reflected energy is wasted. Part of the magic of the TPV is to design a really good mirror that reflects energy back to the source, which is not a concern for solar cells. The current design operates best for a blackbody source around 2000K and there is probably no point in using it at 5600K. Cool stuff.