Topological states in superlattices of HgTe class of materials for engineering three-dimensional flat bands

In search of materials with three-dimensional flat band dispersions, using ab initio computations we investigate how topological phases evolve as a function hydrostatic pressure and uniaxial strain in two types superlattices: HgTe/CdTe HgTe/HgSe. short-period superlattices, our analysis unveils the presence isoenergetic nodal lines, which could host strain-induced bands at Fermi level without requiring doping, when fabricated, for instance, core-shell nanowires. contrast, HgTe/HgSe superlattices are found to harbor rich phase diagram plethora phases. Notably, unstrained superlattice realizes an ideal Weyl semimetal points situated level. A small-gap insulator multiple inversions can be obtained by tuning volume: under compressive strain, material transitions sequentially into Dirac nodal-line semimetal, finally single inversion.