Abstract
We report the condensation of microcavity exciton-polaritons at $\ensuremath{\Gamma}$ points located on the boundary between the third and higher Brillouin zones in hexagonal lattices: triangular and honeycomb geometries. We collect experimental evidence that supports the finite momentum condensation: (1) the coherent Bragg peaks formed at nonzero $\ensuremath{\Gamma}$ points; (2) the nonlinear intensity increase in the exciton-polariton emission at quantum degeneracy threshold; (3) the spectral linewidth behavior: narrowing near threshold and broadening above threshold; and (4) the equivalent 4${f}_{{y}^{3}\ensuremath{-}3{x}^{2}y}$-like orbital symmetry in real space. The $f$-orbital state at $\ensuremath{\Gamma}$ points appears as a metastable momentum valley to trap exciton-polaritons, which is explained by single-particle band-structure calculations.
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