Modeling Thermoelectric Figure of Merit for Quantum Materials Using the Lambert W Function

ABSTRACT Achieving a high figure of merit ( ZT ) in thermoelectric materials requires balancing inherently conflicting material properties, namely electrical conductivity, the Seebeck coefficient, and thermal conductivity. This paper introduces an integrated theoretical framework that leverages polylogarithmic functions and multibranch Lambert W formulations to navigate these conflicting requirements. By extending classical transport models to incorporate energy‐dependent scattering and realistic quantum statistics, we derive closed‐form expressions for key transport coefficients and enable analytical inversion of the reduced chemical potential (). This framework enables extremum analyses that isolate the carrier concentrations and temperature ranges critical for maximizing thermoelectric efficiency. Identifying these parameters paves the way for scalable materials that strengthen sustainable energy harvesting and enhance waste‐heat recovery. This work establishes a foundation for exploring complex quantum materials and next‐generation thermoelectric technologies using a model‐based approach.