  Group-IV monochalcogenides have attracted much attention due to their
potential of ferroelectric and multiferroic properties. Recently,
centrosymmetric gamma-phase GeSe in a double-layer honeycomb lattice has been
theoretically predicted, but the synthesized gamma-phase GeSe showed a
noncentrosymmetric atomic structure, leading to the possibility of
ferroelectricity and spin-splitting. Here, we study the quasiparticle band
structures, spontaneous polarization, and spin-splitting in noncentrosymmetric
gamma-GeSe using density functional theory and GW calculations. Our results
show that noncentrosymmetric few-layer and bulk gamma-GeSe have semiconducting
band structures with indirect band gaps, which depend almost linearly on the
reciprocal of the number of layers. Spontaneous polarization occurs due to a
small charge transfer between the layers, which increases with compressive
strain, and ferroelectric switching can be achieved by an interlayer
translation with a small energy barrier. Spin-splitting is found to be more
significant at the highest valence band than at the lowest conduction band. Our
results provide insights into the fundamental electronic properties of a
layered ferroelectric semiconductor applicable to devices with
ferroelectric/nonferroelectric junctions.
