A quantum hydrodynamic model is used to study the edge modes of chiral Berry plasmons. The transcendental equation of the dispersion relation is solved nonlinearly and semi-analytically. We predict a new one-way chiral edge state with the quantum effect compared to that without the quantum effect, at the both side of $q=0$. Indeed, the plasmon frequencies for positive and negative $q$, exhibit different limits for $qrightarrow 0^{-}$ and $qrightarrow 0^{+}$. As a result, the quantum effect enhances the chirality in the vicinity of $q=0$. Both counterpropagating edge modes exhibit greater confinement to the edge with the quantum effect. In addition, new localized edge modes are found with increased Berry flux in both cases, i.e., without and with the quantum effect.
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