  Topological photonics is an emergent research discipline which interlinks
fundamental aspects of photonics, information processing and solid-state
physics. Exciton-polaritons are a specifically interesting platform to study
topological phenomena, since the coherent light matter coupling enables new
degrees of freedom such as tunable non-linearities, chiralities and
dissipation. Room-temperature operation of such exciton-polaritons relies on
materials comprising both, large exciton binding energies and oscillator
strength. We harness widely spectrally tunable, room temperature
exciton-polaritons based on a WS2 monolayer in an open optical cavity to
realize a polariton potential landscape which emulates the Su-Schrieffer-Heeger
(SSH) Hamiltonian. It comprises a domain boundary hosting a topological,
exponentially localized mode at the interface between two lattices
characterized by different Zak-phases which features a spectral tunability over
a range as large as 80 meV. Moreover, we utilize the unique tilt-tunability of
our implementation, to transform the SSH-lattice into a Stark-ladder. This
transformation couples the topologically protected defect mode to propagating
lattice modes, and effectively changes the symmetry of the system. Furthermore,
it allows us to directly quantify the Zak-phase difference
$\Delta_{Zak}=(1.13\pm 0.11)\pi$ between the two topological phases. Our work
comprises an important step towards in-situ tuning topological lattices to
control and guide light on non-linear chips.
