Band-gap formation and morphing in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>?</mml:mi><mml:mtext>?</mml:mtext><mml:msub><mml:mi>T</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> superlattices

Electrons in $\ensuremath{\alpha}\text{\ensuremath{-}}{T}_{3}$ lattices behave as condensed-matter analogies of integer-spin Dirac fermions. The three atoms making up the unit cell bestow energy spectrum with an additional band that is completely flat, providing unique electronic properties. interatomic hopping term, $\ensuremath{\alpha}$, known to strongly affect two-dimensional (2D) lattice, allowing it continuously morph from graphenelike responses behavior fermions a dice lattice. For pristine lattice structures bands are gapless, but small deviations atomic equivalence sublattices will introduce gaps spectrum. It unknown how these transport and properties such superlattice minibands. Here we investigate dependency on parameter $\ensuremath{\alpha}$ accounting for different symmetry-breaking terms, show affects band-gap formation. Furthermore, find superlattices can force close shift energy. Our results demonstrate provide versatile material 2D engineering purposes.