Intertwined non-trivial band topology and giant Rashba spin splitting

Composite quantum compounds (CQCs) have become an important avenue for the investigation of inter-correlation between two distinct phenomenon in physics. Topological superconductors, axion insulators etc. are few such CQCs which have recently drawn tremendous attention in the community. Topological nontriviality and Rashba spin physics are two different quantum phenomena but can be intertwined within a CQC platform. In this letter, we present a general symmetry based mechanism, supported by \textit{ab-initio} calculations to achieve intertwined giant Rashba splitting and topological non-trivial states simultaneously in a single crystalline system. Such co-existent properties can further be tuned to achieve other rich phenomenon. We have achieved Rashba splitting energy ($\Delta E$) and Rashba coefficient ($\alpha$) values as large as 161 meV and 4.87 eV$\r{A}$ respectively in conjunction with Weyl semimetal phase in KSnSb$_{0.625}$Bi$_{0.375}$. Interestingly, these values are even larger than the values reported for widely studied topologically trivial Rashba semiconductor BiTeI. The advantage of our present analysis is that one can achieve various topological phases without compromising the Rashba parameters, within this CQC platform.