  An efficient approach to improve the thermoelectric performance of materials
is to converge their electronic bands, which is known as band engineering. In
this regard, lots of effort have been made to further improve the
thermoelectric efficiency of bulk and exfoliated monolayers of Bi$_{2}$Te$_{3}$
and Sb$_{2}$Te$_{3}$. However, ultra-high band degeneracy and thus significant
improvement of power factor have not been yet realized in these materials.
Using first-principles methods, we demonstrate that the valley degeneracy of
Bi$_{2}$Te$_{3}$ and Sb$_{2}$Te$_{3}$ can be largely improved upon substitution
of the middle layer Te atoms with the more electronegative S or Se atoms. Our
detailed analysis reveals that in this family of materials two out of four
possible valence band valleys merely depend on the electronegativity of the
middle layer chalcogen atoms, which makes the independent modulation of the
valleys position feasible. As such, band alignment of Bi$_{2}$Te$_{3}$ and
Sb$_{2}$Te$_{3}$ largely improves upon substitution of the middle layer Te
atoms with more electronegative, yet chemically similar, S and Se ones. A
superior valence band alignment is attained in Sb$_{2}$Te$_{2}$Se monolayers
where the three out of four possible valleys are well-aligned, resulting in a
giant band degeneracy of 18 that holds the record among all thermoelectric
materials.
