Abnormal behavior of preferred formation of cationic vacancy from the interior in γ-GeSe monolayer with the stereo-chemical antibonding lone-pair state

Abstract: Two-dimensional (2D) materials tend to have the preferably formation of vacancies at the outer surface. Here, contrary to the normal notion, we reveal a type of vacancy that thermodynamically initiates from the interior part of the 2D backbone of germanium selenide ({\gamma}-GeSe). Interestingly, the Ge-vacancy (VGe) in the interior part of {\gamma}-GeSe possesses the lowest formation energy amongst the various types of defects considered. We also find a low diffusion barrier (1.04 eV) of VGe which is a half of those of sulfur vacancy in MoS2. The facile formation of mobile VGe is rooted in the antibonding coupling of the lone-pair Ge 4s and Se 4p states near the valence band maximum, which also exists in other gamma-phase MX (M=Sn, Ge; X=S, Te). The VGe is accompanied by a shallow acceptor level in the band gap and induces strong infrared light absorption and p-type conductivity. The VGe located in the middle cationic Ge sublattice is well protected by the surface Se layers-a feature that is absent in other atomically thin materials. Our work suggests that the unique well-buried inner VGe, with the potential of forming structurally protected ultrathin conducting filaments, may render the GeSe layer an ideal platform for quantum emitting, memristive, and neuromorphic applications.