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,beta,gamma,delta, and chiral-alpha+delta phases. Among them the gamma and alpha phases were found to be 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 the most stable monolayer gamma phase, 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.