Low lattice thermal conductivity in spinel structures with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi></mml:math>-electron lone pairs

The low thermal conductivity of some semiconducting cubic spinel chalcogenides makes them promising for thermoelectric applications. A key challenge is understanding mechanisms for low thermal conductivity in this class of materials. Here, we theoretically investigated two spinel semiconductors ${\mathrm{CdBi}}_{2}{\mathrm{Se}}_{4}$ and ${\mathrm{PbBi}}_{2}{\mathrm{Se}}_{4}$. We find that these show intrinsic ultra-low lattice thermal conductivities (${\ensuremath{\kappa}}_{l}$) of 0.52--1.24 W ${\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 300 K. We investigated the origin of such low ${\ensuremath{\kappa}}_{l}$ by analyzing the nature of the chemical bonding in relation to the crystal structure. The interaction between $\mathrm{Pb}\text{\ensuremath{-}}6s/\mathrm{Bi}\text{\ensuremath{-}}6s$ and $\mathrm{Se}\text{\ensuremath{-}}4p$ orbitals was found to generate antibonding states below the Fermi level in the electronic band structures resulting in softening of the lattice of these compounds. The lattice dynamics of these compounds exhibit strong acoustic-optical coupling and avoided-crossing features. The presence of additional anticrossing in ${\mathrm{PbBi}}_{2}{\mathrm{Se}}_{4}$ is attributed to strong anharmonic vibrations of the Se atoms as a result of the formation of antibonding states by ${\mathrm{Pb}}^{2+}\phantom{\rule{4pt}{0ex}}{s}^{2}$ active lone pairs with Se. Further, bridging Se atoms between tetrahedra and octahedra have asymmetric, anisotropic potential energy surfaces along the $x, y$, and $z$ directions with strong lattice anharmonicity. The electronic band structure exhibits complex degenerate conduction bands, leading to multiple anisotropic carrier pockets with small transport effective masses. This nontrivial band structure leads to both high Seebeck coefficient and high conductivity. The estimated maximum thermoelectric figure of merit is approximately 1.32 at 500 K in ${\mathrm{PbBi}}_{2}{\mathrm{Se}}_{4}$. These findings offer valuable insights for the future design and exploration of thermoelectric materials with low lattice thermal conductivity.