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The extraordinary properties and the novel applications of black phosphoreneinduce the research interest on the monolayer group-IV monochalcogenides. Hereusing the first-principles calculations, we systematically investigate theelectronic, transport and optical properties of monolayer $\alpha-$ and$\beta-$GeSe, the latter of which was recently experimentally realized. Wefound that, monolayer $\alpha-$GeSe is a semiconductor with direct band gap of1.6 eV, and $\beta-$GeSe displays indirect semiconductor with the gap of 2.47eV, respectively. For monolayer $\beta-$GeSe, the electronic/hole transport isanisotropic with an extremely high electron mobility of 7.84$\times10^4$$cm^2/V\cdot {s}$ along the zigzag direction, comparable to that ofblack phosphorene. Furthermore, for $\beta-$GeSe, robust band gaps nearlydisregarding the applied tensile strain along the zigzag direction is observed.Both monolayer $\alpha-$ and $\beta-$GeSe exhibit anisotropic opticalabsorption in the visible spectrum.

Electronic, transport and optical properties of monolayer $\alpha$ and $\beta-$GeSe: A first-principles study