| Abstract
| - We present first-principles investigations of the origin of the stability of the helical structure of Te throughdetermination of the structure and energetics of its clusters, the largest one comprising 12 Te atoms, andhelical forms. Among all the clusters we have studied, Te8 with a closed-ringlike helical structure is the moststable one; it is even more stable than an infinitely long helix. The stability of the Te structures depends onthe Te−Te−Te bond angle and coordination number of Te atoms. Wannier function-based analysis of thechemical bonding in Te helix reveals sp hybridization giving rise to a σ- and a three-center-π-like bondingbetween neighboring Te atoms. While the former stabilizes a two-fold coordination in the helix, the latterstabilizes a specific Te−Te−Te angle. As a result, the helical structure is stabilized, and closed loops ofhelices are more stable than the open helical chains. A comparative study of the vibrational modes of bulkTe and that of a single helix shows that the rotational mode of bulk Te is significantly softened in the caseof a single helix due to the absence of interhelical interactions in the latter. We estimate the interhelicalinteraction strength in bulk Te to be about 3.0 meV/helix. Relative energies of an infinite helix of Te withrespect to a linear chain show that the coupling of transverse chiral acoustic wave with strain plays a crucialrole in the formation of the helix. We find that bulk Te is more stable to slip deformation than stretchdeformation.
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