Forbidden p-d Orbital Coupling Accelerates High-Power-Factor Materials Discovery

The intrinsic entanglement between electrical conductivity ($\sigma$) and the Seebeck coefficient ($S$) significantly constrains power factor (PF) enhancement in thermoelectric (TE) materials. While high valley degeneracy ($N_{\mathrm{vk}}$) effectively balances $\sigma$ and $S$ to improve PF, identifying compounds with high $N_{\mathrm{vk}}$ remains challenging. In this study, we develop an effective approach to rapid discover $p$-type semiconductors with high $N_{\mathrm{vk}}$ through manipulating anion-$p$ and cation-$d$ orbital coupling. By prohibiting $p$-$d$ orbital coupling at the $\Gamma$ point, the valence band maximum shifts away from the $\Gamma$ point (where $N_{\mathrm{vk}}$=1), thereby increasing $N_{\mathrm{vk}}$. Through the examination of the common irreducible representations of anion-$p$ and cation-$d$ orbitals at the $\Gamma$ point, we identify 7 compounds with $N_{\mathrm{vk}}$ $\ge$ 6 from 921 binary and ternary semiconductors. First-principles calculations with electron-phonon coupling demonstrate that PtP$_2$, PtAs$_2$, and PtS$_2$ exhibit exceptionally high PFs of 130, 127, and 82 $\mu$Wcm$^{-1}$K$^{-2}$ at 300K, respectively, which are three to five times higher than those of the well-studied TE materials. This work not only elucidates the underlying mechanism of high $N_{\mathrm{vk}}$ formation through group theory, but also establishes an efficient high-PF material discovery paradigm, extended to more complex systems.