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

Probing miniband structure and Hofstadter butterfly in gated graphene superlattices via magnetotransport