Motivated by the recent fabrication of a new four-atomic-thick hexagonal polymorph from group IV monochalcogenide, so-called $\gamma$-GeSe [Nano Lett. {\bf 21} (2021) 4305]. In this paper, we propose and examine the structural characteristics, electronic properties, and carrier mobility of monolayers Janus $\gamma$-Ge$_2XY$ ($X/Y =$ S, Se, or Te) based on comprehensive first-principles calculations. Monolayers $\gamma$-Ge$_2XY$ are confirmed to be structurally stable. Our calculations reveal that $\gamma$-Ge$_2XY$ monolayers are indirect semiconductors with Mexican-hat-like dispersions in the top valence band. While the effect of the electric field on the energy band dispersions of $\gamma$-Ge$_2XY$ monolayers is weak, the energy band dispersions are changed drastically in the presence of strain, especially compressive strain. Interestingly, a structural phase transition from semiconductor to metal is observed in $\gamma$-Ge$_2XY$ under compressive strain. $\gamma$-Ge$_2$STe and $\gamma$-Ge$_2$SeTe possess high electron mobility with values of $3.22\times 10^3$ and $8.33\times 10^3$~cm$^2$V$^{-1}$s$^{-1}$, respectively. Our findings not only explore the fundamental physical properties of $\gamma$-Ge$_2XY$ but also open up new opportunities in the design of high-performance electronic nanodevices based on layered nanomaterials with Mexican-hat-like dispersions.
Motivated by transformation of AB-stacking bilayer graphene into fluorinated single-layer diamond (fluorinated diamane C4F2), we investigate the structural, elastic, electronic, transport, and optical properties of fluorinated diamane C4F2 using density functional theory.
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