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In this letter, we predict the emergence of non-trivial band topology in thefamily of XX'Bi compounds having $P\overline{6}2m$ (\# 189) space group. Usingfirst principles calculations within hybrid functional framework, wedemonstrate that NaSrBi and NaCaBi are strong topological insulator undercontrolled band engineering. Here, we propose three different ways to engineerthe band topology to get a non-trivial order: (i) hydrostatic pressure, (ii)biaxial strain (due to epitaxial mismatch), and (iii) doping. Non-triviality isconfirmed by investigating bulk band inversion, topological Z$_2$ invariant,surface dispersion and spin texture. Interestingly, some of these compoundsalso show a three dimensional topological nodal line semi-metal (NLS) state inthe absence of spin orbit coupling (SOC). In these NLS phases, the closed loopof band degeneracy in the Brillouin zone lie close to the Fermi level.Moreover, a drumhead like flat surface state is observed on projecting the bulkstate on the [001] surface. The inclusion of SOC opens up a small band gapmaking them behave like a topological insulator.

Emergence of Topological insulator and Nodal line semi-metal states in XX'Bi (X=Na, K, Rb, Cs; X'=Ca, Sr)