We explore the correlations between velocity and metallicity and the possible distinct chemical signatures of the velocity over-densities of the local Galactic neighbourhood. We use the large spectroscopic survey RAVE and the Geneva Copenhagen Survey. We compare the metallicity distribution of regions in the velocity plane ($v_R,v_phi$) with that of their symmetric counterparts ($-v_R,v_phi$). We expect similar metallicity distributions if there are no tracers of a sub-population (e.g., a dispersed cluster, accreted stars), if the disk of the Galaxy is axisymmetric, and if the orbital effects of the spiral arms and the bar are weak. We find that the metallicity-velocity space of the solar neighbourhood is highly patterned. A large fraction of the velocity plane shows differences in the metallicity distribution when comparing symmetric $v_R$ regions. The typical differences in the median metallicity are of $0.05$ dex with a statistical significance of at least $95%$, and with values up to $0.6$ dex. For low azimuthal velocity $v_phi$, stars moving outwards in the Galaxy have on average higher metallicity than those moving inwards. These include stars in the Hercules and Hyades moving groups and other velocity branch-like structures. For higher $v_phi$, the stars moving inwards have higher metallicity than those moving outwards. The most likely interpretation of the metallicity asymmetry is that it is due to the orbital effects of the bar and the radial metallicity gradient of the disk. We present a simulation that supports this idea. We have also discovered a positive gradient in $v_phi$ with respect to metallicity at high metallicities, apart from the two known positive and negative gradients for the thick and thin disks, respectively.
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