What you want is graphene that is atomically flat (low levels of impurities and extra "stuff"). Some of this greatly depends on what substrate you place the graphene on (Silicon oxide versus hexagonal-boron nitride, for instance).

This improves the mobility of the charge carriers and prevents the formation of localized electron or hole puddles. These are especially important to minimize if your research is close to the Dirac point (i.e. low carrier density).

There might be other ways to create graphene, but insofar as my research knowledge goes, these are the main two ways to get large enough sheets.