  We report on the observation of the magnetic quantum ratchet effect in
graphene with a lateral dual-grating top gate (DGG) superlattice. We show that
the THz ratchet current exhibits sign-alternating magneto-oscillations due to
the Shubnikov-de Haas effect. The amplitude of these oscillations is greatly
enhanced as compared to the ratchet effect at zero magnetic field. The
direction of the current is determined by the lateral asymmetry which can be
controlled by variation of gate potentials in DGG. We also study the dependence
of the ratchet current on the orientation of the terahertz electric field (for
linear polarization) and on the radiation helicity (for circular polarization).
Notably, in the latter case, switching from right- to left-circularly polarized
radiation results in an inversion of the photocurrent direction. We demonstrate
that most of our observations can be well fitted by the drift-diffusion
approximation based on the Boltzmann kinetic equation with the Landau
quantization fully encoded in the oscillations of the density of states.
