Strain tuning of electronic properties of various dimension elemental tellurium with broken screw symmetry

We present a systematical study of atomic structures and electronic properties of various dimension tellurium (Te) with broken intrinsical screw symmetry by applying reasonable strain. It is demonstrated that (i) bulk trigonal Te has degenerate Weyl nodes around the H point near the Fermi energy, and this degeneracy will be broken by introducing the selenium (Se) atom through creating the inner unsymmetrical strain, instead of external shear strain. (ii) 2D structures of tetragonal Te (t-Te) and 1T-MoS2-like Te (1T-Te) show direct and indirect band gap, respectively. Under the uniform biaxial compressive (BC) strain, monolayer of t-Te shows the direct-to-indirect band gap transition, while 1T-Te monolayer has a band gap transition firstly from indirect to direct and then from direct to indirect. Their effective masses of hole and electron can be effectively tuned by BC strain. (iii) One-dimensional (1D) structures of single helix, triangular Te and hexagonal Te nanowires display the obvious quantum confinement effect on the band structure and different sensitivity to the effect of uniaxial compressive strain.