From the topological spin-Hall effect to the non-Hermitian skin effect in an elliptical micropillar chain.

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.