Topological Matter: Graphene and Superfluid $$^3$$ He.

The physics of graphene and of the superfluid phases of $$^3$$ He have many common features. Both systems are topological materials where quasiparticles behave as relativistic massless (Weyl, Majorana or Dirac) fermions. We formulate the points where these features are overlapping. This will allow us to use graphene to study the properties of superfluid $$^3$$ He, to use superfluid $$^3$$ He to study the properties of graphene, and to use both of them in combination to study the physics of topological quantum vacuum. We suggest also some particular experiments with superfluid $$^3$$ He using graphene as an atomically thin membrane impenetrable for He atoms but allowing for spin, momentum and energy transfer. [ABSTRACT FROM AUTHOR]