How to use coul/long correctly?

Please reply to the list no to me, thanks.

I don’t expect to simulate Al2O3 supercell with only Coulombic interactions.

When describing a supercell with an incomplete/incorrect potential there is no guarantee what the pressure value will be. It can be very large or it can be very negative.

Actually, I want to simulate the Al2O3 supercell with the potential Zhou, X. W., Wadley, H. N. G., Filhol, J.-S., & Neurock, M. N. (2004).

This means that it is a modified Streitz-Mintmire potential and you will need to implement its Coulomb integrals and a variable charge capability.

Modified charge transfer–embedded atom method potential for metal/metal oxide systems. Physical Review B, 69(3), 035402. doi:10.1103/PhysRevB.69.035402.
In the paper, the potential considers the coulombic interaction. On the other hand, LAMMPS can handle the coulombic interaction.
I tried to use hybrid/overlay to combine coul/long and the other part of the potential.

Sorry but the Coulomb potential in their paper does not use point charges but Slater type orbitals, which means you cannot use coul/long.

The other part of the potential was written by myself.
During the test, the potential energy of the potential energy goes right, while the press goes wrong.

This is a serious problem and needs to be corrected first. This means your code is not conserved so that energy and forces go opposite directions. I suggest you check the signs of force expressions in your code.

Hence, I decided to check the coul/long part with my own result(~1GPa).

Your own result of coul/long in your own code? I am not convinced that 1 GPa is a reasonable value.