  The topological spin-Hall effect causes different spins to propagate in
opposite directions based on Hermitian physics. The non-Hermitian skin effect
causes the localization of all modes of a system at its edges. Although these
effects have separately attracted tremendous interest, their completely
different origins have made them hard to observe in a single system. Here we
propose a system based on exciton-polariton elliptical micropillars hosting
both the effects. The polarization splitting and different orientation of the
elliptical micropillars naturally give rise to the topological spin-Hall effect
in a one dimensional lattice. By making the effective decay rates of the
different spin ($\sigma_\pm$) modes unequal, the system makes a phase
transition from the Hermitian regime to non-Hermitian regime showing the
non-Hermitian skin effect.
