Thermal Conductivity in the Z direction shows large value for a 10*1 graphene sheet;where the expected z component should be small(tends to zero).The system seems stable but couldn’t figure out where the problem is!I It will be great to get some help regarding the issue.Thanks in advance.

Your description is far to vague for giving any meaningful advice.

Please provide some more details about your simulation setup, the method used to compute thermal conductivity and - ideally - your input files and some information on how you validated that those are working correctly and that your results are statistically converged.

Tersoff potential was used,first the system was thermally stabilized fixing nvt and then fixing nve energy minimization was done.I used Green-Kubo method to compute the thermal conductivity.By observing temperature,pressure,energy values in the log.lammps file,decaying characteristics of the HCACF function and no broken structure visualization in ovito,I assumed that the system is stable!!

That helps, but not a lot. I am particularly interested in the geometry. Can you create a visualization of it?

Have you checked for finite size effects, especially in z direction? What happens to your results if you replicate the system in z?