In the weak interaction limit, behaviors of electrons can still be described by a 1-partitcle equation with a modified mass, where the change in mass can be understood as effects of other neighboring electrons as a single electron drags along. Since the cluster of electrons couples to gravity as usual, then the effective mass of a quasi-particle couples to gravity in the same way as that of a genuine electron. Moreover, the effective mass can be negative which is the case of holes which are “bubbles” in the electron liquid.
In graphene, there are massless Dirac electrons. Do they couple to the gravity?
I think what I intended to ask should be "How to incorporate effects of gravity in a many-electron system?"
(Originally I asked "do effective masses couple to gravity?")