Search for the metal-weak thick disk from the LAMOST DR5

Based on the data release of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope survey (LAMOST DR5) and the \emph{Gaia} Early Data Release 3 (\emph{Gaia} EDR3), we construct a sample containing 46,109 giant (log~$\emph{g}$ $\leqslant$ 3.5\,dex) stars with heliocentric distance d $\leqslant$ 4 kpc, and the sample is further divided into two groups of the inner ({\RGC} $<$ 8.34 \,kpc) and outer region ({\RGC} $>$ 8.34\,kpc). The {\LZ} distributions of our program stars in the panels with different [Fe/H] and [$\alpha$/Fe] suggest that the thick-disk consists of two distinct components with different chemical compositions and kinematic properties. For the inner region, the metal-weak thick disk (MWTD) contributes significantly when [$\alpha$/Fe] $>+$0.2\,dex and [Fe/H] $<-$0.8\,dex, while the canonical thick-disk (TD) dominates when [Fe/H]$>-$0.8\,dex. However, MWTD clearly appears only when [$\alpha$/Fe] $>+$0.2\,dex and [Fe/H] $<-$1.2\,dex for the outer region, and its proportion is lower than that of the inner region within the same metallicity. Similar result can be obtained from the {\VP} distribution. The high fraction of MWTD in the inner than that in the outer region imply that MWTD may form in the inner disk, and is an observational evidence about the inside-out disk formation scenario.