Two-dimensional Haeckelite GeS with high carrier mobility and exotic polarization orders

Two-dimensional (2D) group-IV monochalcogenides have raised the attention of the material science community owing to their rich physical properties and promising applications in 2D functional devices. Based on ab initio calculations, we explore three square/octagon Haeckelite structures as additional stable allotropes of 2D GeS. All the predicted allotropes are semiconducting with wide [2.5-2.7 eV at the Heyd-Scuseria-Ernzerhof exchange-correlation functional (HSE06) level] and tunable band gaps. Meanwhile, h(1)- and h(2)-GeS exhibit unusually high carrier mobilities up to 10(4) cm(2) V-1 s(-1). Exotic electric polarization orders, including antiferro-electricity and noncollinear polarization with atomic-scale dipole vortices, are found in the predicted allotropes. All three Haeckelite allotropes can be connected to the corresponding hexagonal GeS allotropes laterally with an extremely low energy cost, which indicates the possibility for the coexistence of different phases and the formation of heterostructures in the same GeS layer.