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Topological Insulators with gapless surface states and insulating bulk innon-centrosymmetric cubic systems have been extensively explored following thediscovery of two-dimensional quantum spin hall effect in zincblende HgTe. Insuch systems the negative band inversion strength E$_{BIS}$ ($=$ E$_{\Gamma_6}-$ E$_{\Gamma_8} <$ 0) governs the robustness of the non-trivial topologicalstates at ambient conditions. Hence, realizing large negative values ofE$_{BIS}$ has been a guiding motivation of several investigations reported inliterature. Here, we present a material design approach which can be employedto realize large negative values of E$_{BIS}$ in cubic materials such ashalf-Heusler (HH) oxides with 18 valence electron configurations. We explore 27HH oxides of the form ABO (A = Li, K, Rb; B = Cu, Ag, Au) in $\alpha$-,$\beta$-, and $\gamma$-phase (by placing transition metal atom at differentWyckoff positions) for their non-trivial topological phase. Off these threephases, we found that, the $\alpha$-phase of nine HH oxides (wherein thetransition metal atoms occupy 4a Wyckoff positions in the crystal structure) isthe most promising with non-trivial topological phase which is governed by themass-darwin relativistic effects enhancing E$_{BIS}$. Whereas the other phaseswere found to be either trivial semiconductors or semimetals or metals and mostof them being dynamically unstable. We focus on RbAuO in $\alpha$-phase withE$_{BIS}$ of $-$ 1.29 eV and the effect of strain fields on the topologicalsurface states of this compound. We conclude that the $\alpha$-phase of HHoxide presented here can be synthesized experimentally for diverse roomtemperature applications in spintronics and nanoelectronics.

Non-trivial topological phases in transition metal rich half-Heusler Oxides