# Interplay between Structural, Electronic, and Topological Properties in Low-Dimensional Tellurium

## TL;DR

This paper explores how tellurium's structure, electronic properties, and topology change across different dimensions, revealing new topological phases.

## Contribution

The study identifies new topological phases in tellurium across dimensions, including incipient quantum spin Hall behavior and Weyl nodes.

## Key findings

- Bulk Te–I is a narrow-gap semiconductor with Weyl nodes and chiral phonon behavior.
- Buckled kagome and square tellurene lattices show nontrivial Z2=1 topology.
- Hydrogen-passivated hexagonal tellurene exhibits a robust quantum spin Hall phase.

## 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 (
Z2=0
), 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
Z2=1
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
Z2=1
invariant, preserved under applied strain
and chemical functionalization. In the one-dimensional limit, helical
tellurium nanowires preserve chirality and host edge-localized 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, two-dimensional quantum spin Hall
and incipient
Z2
phases, and one-dimensional helical systems.