Enhanced thermoelectric performance by lone-pair electrons and bond anharmonicity in the two-dimensional Ge2Y2 family of materials with Y=N

Using density functional theory combined with the Boltzmann transport equation, the charge, thermal transport, and thermoelectric properties in two-dimensional (2D) ${\mathrm{Ge}}_{2}{Y}_{2}$ ($Y=\text{N}$, P, As, or Sb) monolayers characterized by two structural phases, i.e., $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ge}}_{2}{\mathrm{Y}}_{2}$ and $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ge}}_{2}{\mathrm{Y}}_{2}$, have been studied systematically. Our theoretical results demonstrate that the lone-pair electrons have remarkable influences on their lattice thermal conductivity. By performing comparative studies on the two different structures of ${\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}$, we uncover that the above influences not only originate from the interactions between the lone-pair electrons around Sb atoms and the bonding electrons of the adjacent Ge atom, but also from the interlayer Coulomb repulsive forces of lone-pair electrons distributed in different layers. The latter leads to a strong anharmonicity, which greatly suppresses the lattice thermal conductivity. Thus, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}$ monolayer has an ultralow thermal conductivity with 0.19 W/mK, while $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}$ monolayer with 5.1 W/mK at the temperature 300 K. Owing to the ultralow lattice thermal conductivity induced by lone-pair electrons, the predicted maximum value of the thermoelectric figure of merit ($ZT$) reaches 1.2 for $p$-type and 1.18 for $n$-type doping $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}$. Our theoretical results put forward another effective mechanism to design and optimize 2D thermoelectric materials with high thermoelectric conversion efficiency.