Two ultra-stable novel allotropes of Tellurium few-layers

At least four two- or quasi-one- dimensional allotropes and a mixture of them were theoretically predicted or experimentally observed for low-dimensional Te, namely the {\alpha}, \b{eta}, {\gamma}, {\delta} and chiral-{\alpha}+{\delta} phases. Among them the {\gamma} and {\alpha} phases were found the most stable phases for monolayer and thicker layers, respectively. Here, we found two novel low-dimensional phases, namely the {\epsilon} and {\zeta} phases. The {\zeta} phase is over 29 meV/Te more stable than and the {\epsilon} phase shows comparable stability with the most stable monolayer {\gamma} phase. The energetic difference between the {\zeta} and {\alpha} phases reduces with respect to the increased layer thickness and vanishes at the four-layer (12-sublayer) thickness, while this thickness increases under change doping. Both {\epsilon} and {\zeta} phases are metallic chains and layers, respectively. The {\zeta} phase, with very strong interlayer coupling, shows quantum well states in its layer-dependent bandstructures. These results provide significantly insight into the understanding of polytypism in Te few-layers and may boost tremendous studies on properties of various few-layer phases.