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 $$ , assuming that the efficiency is mainly determined by this single parameter. Here, we show that the thermoelectric conversion efficiency is determined by three independent parameters, $$ , τ, and β, which we call the three thermoelectric degrees of freedom (DoFs). $$ is the well-defined mean of the traditional $$ under nonzero temperature differences. The two additional parameters τ and β 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 τ and β, beyond $$ .