Is Thermoelectric Conversion Efficiency of a Composite Bounded by its Constituents?

We analyze the conversion efficiency of thermoelectric composites, and conclude that thermoelectric figure of merit ZT as we know it is ill-defined for composites, and is irrelevant for their conversion efficiency. In addition, we prove that thermoelectric conversion efficiency of a composite is not bounded by its constituents, and can be higher than all its constituents in the absence of size and interface effects, in contrast to previous claim. Conditions on constituent phases for enhanced conversion efficiency in layered composites are also identified, and the upper bound on their conversion efficiency is established. This points to a new route for high efficiency thermoelectric materials.