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I have created a graphene supercell using Quantum Espresso and performed a vc-relaxation on it. Now, I need to verify whether the created structure is stable and demonstrate its stability with numerical values. Can I use formation or cohesive energy for this purpose?

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    $\begingroup$ check phonon DOS and elastic constants for dynamical and mechanical stability $\endgroup$ Commented Apr 18 at 6:55

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You might want to be more specific about the type of stability you are thinking of. The formation energy would be useful for assessing thermodynamic stability. It sounds as though dynamic and elastic stability might be more what you would want to look at (c.f. Pranav kumar's comment), i.e. that some small atomic displacement or strain is not going to drastically change the structure.

For dynamical stability, you'd want to do a phonon calculation and check if you have any soft modes (see ProfM's answer here).

For elastic stability, you'd want to calculate the elastic constants and check if they obey the Born stability conditions. A good reference specific to 2D materials is Marcin Ma┼║dziarz 2019 2D Mater. 6 048001.

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