Thermoelectric degrees of freedom determining thermoelectric efficiency.

For over half a century, the development of thermoelectric materials has based on the dimensionless figure of merit , assuming that the efficiency is mainly determined by this single parameter. Here, we show that the thermoelectric conversion efficiency is determined by independent parameters, , , and , which we call the three thermoelectric degrees of freedom (DoFs). is the well-defined of the traditional under nonzero temperature differences. The two additional parameters and are gradients of material properties and crucial to evaluating the heat current altered by nonzero Thomson heat and asymmetric Joule heat escape. Each parameter is a figure of merit. Therefore, increasing one of the three DoFs leads to higher efficiency. Our finding explains why the single-parameter theory is inaccurate. Further, it suggests an alternative direction in material discovery and device design in thermoelectrics, such as high and , beyond .