Interplay between structural, electronic, and topological properties in low-dimensional tellurium

Abstract

We present a comprehensive first-principles investigation of the structural, electronic, vibrational, and topological properties of tellurium across its dimensional hierarchy, including bulk trigonal Te−I, two-dimensional tellurene polymorphs, and one-dimensional helical nanowires. Using density functional theory with full inclusion of spin−orbit coupling, we confirm that bulk Te−I is a narrow-gap semiconductor hosting Weyl nodes arising from broken inversion symmetry and degenerate phonon modes suggestive of chiral phonon behavior. In contrast, two-dimensional α- and β-tellurene are found to be topologically trivial ( = 0 2 ), with no spin−orbit-driven band inversion in the occupied manifold. Beyond these established phases, we find that buckled kagome and buckled square tellurene lattices exhibit a nontrivial two-dimensional = 1 2 topology of the occupied electronic bands, indicating incipient quantum spin Hall character in metallic systems. In contrast, one-sided hydrogen-passivated hexagonal tellurene realizes a fully gapped quantum spin Hall phase with a robust = 1 2 invariant, preserved under applied strain and chemical functionalization. In the one-dimensional limit, helical tellurium nanowires preserve chirality and host edgelocalized states accompanied by pronounced anisotropy in carrier effective masses. These results establish tellurium as a highly tunable platform for engineering topological phenomena across dimensionality, bridging three-dimensional Weyl physics, twodimensional quantum spin Hall and incipient 2 phases, and one-dimensional helical systems