Would this be usable for improving heat pumps as well (i.e. for heating the building instead of cooling it)? It is my understanding that they basically work as "reverse refrigerators", and that current designs are able to move about four times as much heat energy as they consume. Would this be able to improve their efficiency even more, or is there something about the thermodynamics that I have missed?
This doesn't aim to improve efficiency. Most refrigerators use phase change of volatile liquids to gases and back again. Most suitable liquids were toxic and/or flammable, so chemists invented the much safer replacement of fully halogenated hydrocarbons (CFCs). The first to gain widespread use was R-12: dichlorodifluoromethane (a.k.a. Freon). CFCs turned out to break down in the upper atmosphere, releasing chlorine that catalyzed destruction of ozone. The worst ones were banned under the Montreal Protocol treaty, and less damaging partially halogenated hydrocarbons (HCFCs and HFCs) were developed as a replacement, e.g. R-22. Modern HFCs like R-134a have even lower ozone depleting potential.
However, ozone depletion isn't the only problem. CFCs/HCFCs/HFCs are also very effective greenhouse gases, often trapping thousands of times more heat than CO2. In an attempt to solve this problem, another class of refrigerants was invented: the hydrofluoroolefins (HFOs). These have low ozone depletion potential, and low global warming potential, but they are somewhat controversial because they compromise the excellent safety of the earlier halogenated refrigerants.
Solid state refrigeration avoids the whole problem, so if it's possible without harming efficiency, as the article suggests, then it's an obviously good idea.
> somewhat controversial because they compromise the excellent safety of the earlier halogenated refrigerants.
I suspect that modern refrigerators designs/manufacturing can negate a much of that. Higher efficiency better insulation means less refrigerant. Better construction means lower chances of a leak. And flammability of HC refrigerants varies wildly. All you really want to if there is a leak not to create a flammable mixture in a standard sized room.
As far as I understand it, "green material" doesn't mean it's more efficient in operation, it just means that it would be less harmful at the end of the system's life. When HFCs from air conditioners, heat pumps, refrigerators, etc. are released into the atmosphere (often when the system is disposed of) they have a disproportionately high greenhouse gas effect compared to vehicle emissions and other common sources.