Composite quantum compounds (CQCs) have emerged as a key tool for examining the interactions between two different physical phenomena. Some of these CQCs that have lately received a lot of community attention are topological superconductors and axion insulators, among others. Despite being two distinct quantum phenomena, Rashba spin physics and topological nontriviality can coexist in a CQC platform. In this work, we have performed ab initio calculations to discover materials that inherit both giant Rashba splitting and topological nontrivial states in a single crystalline system, coined as intrinsic CQCs. In this regard, we have investigated two materials, RbSnBi and CsSnBi, that are found to be strong topological insulators along with giant Rashba splitting energy in valence bands (133 and $228\phantom{\rule{0.16em}{0ex}}\text{meV}$, respectively) with Rashba coefficient ${\ensuremath{\alpha}}_{\mathrm{R}}$ to be 4.26 and $6.4\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4.pt}{0ex}}\text{eV}\phantom{\rule{4.pt}{0ex}}\AA{}$, respectively. These values of ${\ensuremath{\alpha}}_{\mathrm{R}}$ are quite large, and the Rashba coefficient of CsSnBi is the largest, corresponding to valance bands, among previously reported topological materials. Coexisting characteristics of Rashba spin physics and topological nontriviality have the potential to unveil new physical phenomena. For both RbSnBi and CsSnBi, the topological insulating state is found to be associated with coexisting multiple band inversion and multiple Dirac surface states.
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