Abnormal volumetric thermal expansion in the hourglass fermion materials KHgAs and KHgSb

Using first principles density functional theory calculations combined with quasi-harmonic approximation, we demonstrate that the recently reported nonsymmorphic ``hourglass fermion'' materials $\text{KHg}X$ $(X=\mathrm{As}$, Sb) belong to a type of negative thermal expansion (NTE) material with an abnormal volumetric thermal expansion. It is revealed that the NTE is caused by the peculiar layered structures of KHgAs and KHgSb, composed of alternately arranged alkali metal and Hg-$X$ atomic layers with residual tensions. Specifically, the coefficients of negative thermal expansion (CNTE) of KHgAs and KHgSb can reach up to $\ensuremath{-}2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ and $\ensuremath{-}4.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ along the $a$ axis, respectively, as well as a larger volumetric CNTE of $\ensuremath{-}4.98\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ for KHgSb. The analyses of Gr\"uneisen parameters and vibrational modes show that the NTE of $\text{KHg}X$ is driven by the cooperation of membrane and tension effects. It is most likely that the weaker bonds in the Hg-$X$ layer and the smaller mass of alkali metal facilitate the membrane and tension effects, therefore producing a large NTE. Our findings offer insights for understanding the underlying mechanism of NTE behavior in the hourglass fermion materials $\text{KHg}X$.