Is thermoelectric conversion efficiency of a composite bounded by its constituents

We analyze the conversion efficiency of a bilayered thermoelectric composite, and conclude 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. Conditions on constituent phases for enhanced conversion efficiency are also identified, and the upper bound on their conversion efficiency is established. This points to a new route for high efficiency thermoelectric materials.