We study a sample of 17 z > 1.5 absorbers selected based on the presence of strong C i absorption lines in Sloan Digital Sky Survey ( SDSS ) spectra and observed with the European Southern Observatory Very Large Telescope ( ESO-VLT ) spectrograph X-shooter .
We derive metallicities , depletion onto dust , and extinction by dust , and analyse the absorption from Mg ii , Mg i , Ca ii , and Na i that are redshifted into the near infrared wavelength range .
We show that most of these C i absorbers have high metallicity and dust content .
We detect nine Ca ii absorptions with W ( Ca ii \lambda 3934 ) > 0.23 Å out of 14 systems where we have appropriate wavelength coverage .
The observed equivalent widths are similar to what has been measured in other lower redshift surveys of Ca ii systems .
We detect ten Na i absorptions in the 11 systems where we could observe this absorption .
The median equivalent width ( W ( Na i \lambda 5891 ) = 0.68 Å ) is larger than what is observed in local clouds with similar H i column densities but also in z < 0.7 Ca ii systems detected in the SDSS .
The systematic presence of Na i absorption in these C i systems strongly suggests that the gas is neutral and cold , maybe part of the diffuse molecular gas in the interstellar medium ( ISM ) of high-redshift galaxies .

Most of the systems ( 12 out of 17 ) have W ( Mg ii \lambda 2796 ) > 2.5 Å and six of them have log N ( H i ) < 20.3 , with the extreme case of J1341+1852 that has log N ( H i ) = 18.18 .
The Mg ii absorptions are spread over more than \Delta v \sim 400 km s ^ { -1 } for half of the systems ; three absorbers have \Delta v > 500 km s ^ { -1 } .
The kinematics are strongly perturbed for most of these systems , which probably do not arise in quiet disks and must be close to regions with intense star-formation activity and/or are part of interacting objects .
All this suggests that a large fraction of the cold gas at high redshift arises in disturbed environments .