First-principles study on the electronic, optical, and transport properties of monolayer $\alpha$- and $\beta$-GeSe

The extraordinary properties and the novel applications of black phosphorene induce the research interest in the monolayer group-IV monochalcogenides. Here using first-principles calculations, we systematically investigate the electronic, transport, and optical properties of monolayer $\alpha$- and $\beta$-GeSe, revealing a direct band gap of 1.61 eV for monolayer $\alpha$-GeSe and an indirect band gap of 2.47 eV for monolayer $\beta$-GeSe. For monolayer $\beta$-GeSe, the electronic/hole transport is anisotropic, with an extremely high electron mobility of $2.93\times {10}^4{\text{cm}}^2/\text{V}\text{s}$ along the armchair direction, comparable to that of black phosphorene. Furthermore, for $\beta$-GeSe, robust band gaps nearly independent of the applied tensile strain along the armchair direction are observed. Both monolayer $\alpha$- and $\beta$-GeSe exhibit anisotropic optical absorption in the visible spectrum.

Figure 1

Atomic structure of monolayer $\alpha$- and $\beta$-GeSe in a $2\times 2\times 1$ supercell from (a) and (c) the top view and (b) and (d) side view, respectively. The $a$ ($b$) direction is the zigzag (armchair) direction. The blue and green balls denote Ge and Se atoms, respectively.

Figure 2

(a) and (d) PBE calculations with and without SOC of the electronic band structure and PBE calculated density of states (DOS) of monolayer $\alpha$-GeSe and $\beta$-GeSe along high-symmetry directions, respectively. (b) and (e) Electronic band structures under the HSE06 hybrid functional of monolayer $\alpha$-GeSe and $\beta$-GeSe, respectively. (c) and (f) HSE06 band calculations with SOC.

Figure 3

Isosurface plots of the charge density of (a) and (b) CBM and (c) and (d) VBM for monolayer $\alpha$-GeSe and (e) and (f) CBM and (g) and (h) VBM for monolayer $\beta$-GeSe illustrated in the $ab$ and $bc$ planes, with an isovalue of 0.007 $e/{\text{Å}}^3$.

Figure 4

Electronic band structures of monolayer $\alpha$-GeSe under applied strains along (a) the $a$ direction, (b) the $b$ direction, and (c) the $bi$ direction. (d) The evolution of band gaps for $\alpha$-GeSe as a function of the applied strain.

Figure 5

Electronic band structures of monolayer $\beta$-GeSe under applied strains along (a) the $a$ direction, (b) the $b$ direction, and (c) the $bi$ direction. (d) The evolution of band gaps for $\beta$-GeSe as a function of the applied strain.

Figure 6

(a) Top view of 3D ELF and 2D ELF profiles of monolayer $\beta$-GeSe along the (b) $a$ and (c) $b$ directions.

Figure 7

Dependence of band edges with respect to vacuum as a function of applied uniaxial strains along the $a$ and $b$ directions for monolayer (a) $\alpha$- and (b) $\beta$-GeSe. (c) and (d) The relationship between the total energy and strain along the $a$ and $b$ directions for $\alpha$- and $\beta$-GeSe, respectively.

Figure 8

HSE06 calculations of (a) optical absorption spectra and (b) the reflectivity of monolayer $\alpha$- and $\beta$-GeSe for incident light with the polarization along the $a$ and $b$ directions.