  Layered hexagonal Gamma--GeSe, a new polymorph of GeSe synthesized recently,
shows strikingly high electronic conductivity in its bulk form (even higher
than graphite) while semiconducting in the case of monolayer (1L). In this
work, by using first-principles calculations, we demonstrate that, different
from its orthorhombic phases of GeSe, the Gamma--GeSe shows a small spatial
anisotropic dependence and a strikingly thickness-dependent behavior with
transition from semimetal (bulk, 0.04 eV) to semiconductor (1L, 0.99 eV), and
this dual conducting characteristic realized simply with thickness control in
Gamma-GeSe has not been found in other 2D materials before. The lacking of
d-orbital allows charge carrier with small effective mass (0.16 m0 for electron
and 0.23 m0 for hole) which is comparable to phosphorene. Meanwhile, 1L
Gamma--GeSe shows a superior flexibility with Young's modulus of 86.59 N/m,
only one-quarter of that of graphene and three-quarters of that of MoS2, and
Poisson's ratio of 0.26, suggesting a highly flexible lattice. Interestingly,
1L Gamma-GeSe shows an in-plane isotropic elastic modulus inherent with
hexagonal symmetry while an anisotropic in-plane effective mass owing to
shifted valleys around the band edges. We demonstrate the feasibility of strain
engineering in inducing indirect-direct and semiconductor-metal transitions
resulting from competing bands at the band edges. Our work shows that the free
1L Gamma-GeSe shows a strong light absorption (~106 cm-1) and an indirect
bandgap with rich valleys at band edges, enabling high carrier concentration
and a low rate of direct electron-hole recombination which would be promising
for nanoelectronics and solar cell applications.
