Exact Algebraic Decoupling of Electron-Phonon Transport and Maximization of Thermoelectric Figure of Merit (ZT) via Seonggil Phonon Spectrum Engineering and Numerical Validation

The thermoelectric figure of merit, ZT = S^2σT/κ, has historically been constrained by the Wiedemann-Franz law, which rigidly couples electrical conductivity (σ) and thermal conductivity (κ). In this paper, we break this fundamental constraint by applying Seonggil Matrix Theory to solid-state transport phenomena. By algebraically separating the electron transport matrix from the phonon (lattice vibration) scattering matrix within the Rough Operator Algebra (ROA) space, we engineer an asymmetric scattering tensor. This topological meta-structure induces selective destructive interference exclusively for phonon propagationwhle maintaining constructive coherence for electron tunneling, theoretically allowing the lattice thermal conductivity to approach zero (κ_ph → 0) and effectively unbounded ZT maximization. Furthermore, we provide a complete numerical simulation framework validating the dramatic suppression of lattice thermal conductivity and the resulting explosive ZTenhancement at room temperature.