The best COP that can be achieved is related to the Carnot thermal efficiency. See wikipedia "Thermal Efficiency", for example.
If the source of heat is 273K (freezing) and the sink is 318K (heat pump flow temperature of 45C) then the limiting COP value is 318/(318-273) = 7. This is the ideal value - it can never be achieved. A COP value of 4, as commonly achieved in practice, is respectable, suggesting an overall system efficiency of 4/7 or 57%.
However, a claimed COP of 14 breaks fundamental laws of physics. The article does not state what the two temperatures were (source and sink), but if very close, then a high COP figure would be possible, although not very useful. It is a pity that the article does not supply this information.
A semiconductor heat pump would reduce the amount of moving parts, but the source and sink would still need fans and circulators to work.
It is an interesting article, but the headline claims discredit the research, which is a pity.