- Good thermal insulator - Good electrical conductor - Good semiconductor
This is because the hot & cold sides are sandwiched closely together as a PN junction, so once you move heat from one side to the other, it just leaks right back. Mechanical cooling doesn't have this problem, because the hot & cold sides are separated by thin bits of tubing. This makes the thermal leakage a "minor annoyance" in a mechanical system as opposed to "literally the whole problem we're trying to solve" as it is with thermoelectrics.
One work-around is to stack lots & lots of thermoelectric coolers on top of each other. That reduces the temperature difference at each individual PN junction, which in turn lowers the leakage. That's what this team is doing, but using layers that are only a few nanometers thick, so they can fit dozens or hundreds of junctions in a single package.