Complete topological phase diagram and realization of minimum Weyl nodes in a sheared chiral crystal of elemental tellurium

Ideal Weyl semimetals, with minimum Weyl nodes located far away from each other in reciprocal space and near the Fermi level in the energy space, are considered to be crucial for revealing the intrinsic physical properties of Weyl semimetals. Based on first-principles calculations, we demonstrate that elemental tellurium, under application of a broad range of shear strain, is a candidate for realizing ideal Weyl semimetals. Particularly, the sheared elemental tellurium has only four Weyl nodes in the Brillioun zone, which is the minimum number of Weyl nodes that can be achieved by a system with time-reversal symmetry. More importantly, by adjusting the strength of the strain, we obtain abundant topological phases, i.e., Weyl semimetals, strong topological insulators, composite Weyl semimetals, and weak topological insulators in elemental tellurium. Notably, this paper proposes implementing a weak topological insulator phase in a space group with only time-reversal symmetry. The complete topological phase diagram of sheared tellurium is given and the topological properties of different topological nontrivial phases are characterized, respectively.