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We select 1,052,469 (754,635) thin disk stars from {\it Gaia} eDR3 and LAMOSTDR7 in the range of Galactocentric radius $R$ (guiding center radius$R_\mathrm{g}$) from 8 to 11\,kpc to investigate the asymmetries between theNorth and South of the disk midplane. More specifically we analyze the verticalvelocity dispersion profiles ($\sigma_{v_{z}}(z$)) in different bins of $R$($R_\mathrm{g}$) and $[\mathrm{Fe/H}]$. We find troughs in the profiles of$\sigma_{v_{z}}(z)$ located in both the North ($z \sim 0.7$\,kpc) and South ($z\sim -0.5$\,kpc) of the disk at all radial and chemical bins studied. Thedifference between the Northern and Southern vertical velocity dispersionprofiles ($\Delta\sigma_{v_{z}}(|z|)$) shows a shift between curves ofdifferent $R$ and $R_\mathrm{g}$. A similar shift exists in these NS asymmetryprofiles further divided into different $[\mathrm{Fe/H}]$ ranges. The samplebinned with $R_\mathrm{g}$ more clearly displays the features in the velocitydispersion profiles. The shift in the peaks of the $\Delta\sigma_{v_{z}}$profiles and the variation in the phase spiral shape binned by metallicityindicate the variation of the vertical potential profiles and the radialmetallicity gradient. The wave-like signal in NS asymmetry of$\sigma_{v_{z}}(z)$ largely originates from phase spiral; while the NSasymmetry profiles of [Fe/H] only display a weak wave-like feature near solarradius. We perform a test particle simulation to qualitatively reproduce theobserved results. A quantitative explanation of the NS asymmetry in themetallicity profile needs careful consideration of the spiral shape and theperturbation model, and we leave this for future work.

North-South asymmetries in the Galactic thin disk associated with the vertical phase spiral as seen using LAMOST-Gaia stars