Controllable spin splitting in 2D Ferroelectric few-layer {γ}$-GeSe

$\gamma$-GeSe is a new type of layered bulk material that was recently successfully synthesized. By means of density functional theory first-principles calculations, we systematically studied the physical properties of two-dimensional (2D) few-layer $\gamma$-GeSe. It is found that few-layer $\gamma$-GeSe are semiconductors with band gaps decreasing with increasing layer number; and 2D $\gamma$-GeSe with layer number $n\ge 2$ are ferroelectric with rather low transition barriers, consistent with the sliding ferroelectric mechanism. Particularly, spin-orbit coupling induced spin splitting is observed at the top of the valence band, which can be switched by the ferroelectric reversal; furthermore, their negative piezoelectricity also enables the regulation of spin splitting by strain. Finally, excellent optical absorption was also revealed. These intriguing properties make 2D few-layer $\gamma$-GeSe promising in spintronic and optoelectric applications.