  The presence of periodic modulation in graphene leads to a reconstruction of
the band structure and formation of minibands. In an external uniform magnetic
field, a fractal energy spectrum called Hofstadter butterfly is formed.
Particularly interesting in this regard are superlattices with tunable
modulation strength, such as electrostatically induced ones in graphene. We
perform quantum transport modeling in gate-induced square two-dimensional
superlattice in graphene and investigate the relation to the details of the
band structure. At low magnetic field the dynamics of carriers reflects the
semi-classical orbits which depend on the mini band structure. We theoretically
model transverse magnetic focusing, a ballistic transport technique by means of
which we investigate the minibands, their extent and carrier type. We find a
good agreement between the focusing spectra and the mini band structures
obtained from the continuum model, proving usefulness of this technique.
%positions of van Hove singularities at high magnetic field the calculated
four-probe resistance fit the Hofstadter butterfly spectrum obtained for our
superlattice. Our quantum transport modeling provides an insight into the mini
band structures, and can be applied to other superlattice geometries.
