Controllable spin splitting in 2D Ferroelectric few-layer ${$\gamma}$-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 $n \geq 2$ 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.