  Recently realized higher order topological insulators have taken a surge of
interest among the theoretical and experimental condensed matter community. The
two-dimensional second order topological insulators give rise to
zero-dimensional localized corner modes that reside within the band gap of the
system along with edge modes that inhabit a band edge next to bulk modes.
Thanks to the topological nature, information can be trapped at the corners of
these systems, which will be unhampered even in the presence of disorder. Being
localized at the corners, the exchange of information among the corner states
is an issue. Here we show that the nonlinearity in an exciton polariton system
can allow the coupling between the different corners through the edge states
based on optical parametric scattering, realizing a system of multiple
connectible topological modes.
