The Nature of Bonding in Bulk Tellurium Composed of One-Dimensional Helical Chains

Bulk tellurium (Te) is composed of one-dimensional (1D) helical chains which have been considered to be coupled by van der Waals (vdW) interactions. However, based on first-principles density-functional theory calculations, we here propose a different bonding nature between neighboring chains: i.e., the helical chains made of normal covalent bonds are connected together by coordinate covalent bonds. It is revealed that the lone pairs of electrons of Te atom participate in forming coordinate covalent bonds between neighboring chains. Therefore, each Te atom behaves as both electron donor to neighboring chains and electron acceptor from neighboring chains. This ligand-metal-like bonding nature in bulk Te results in the same order of bulk moduli along the directions parallel and perpendicular to the chains, contrasting with the large anisotropy of bulk moduli in vdW crystals. We further find that the electron effective masses parallel and perpendicular to the chains are almost the same each other, consistent with the observed nearly isotropic electrical resistivity. It is thus demonstrated that the normal/coordinate covalent bonds parallel/perpendicular to the chains in bulk Te lead to a minor anisotropy in structural and transport properties, distinct from a strong anisotropy observed in the typical two-dimensional (2D) vdW materials such as graphite and MoS$_2$.