![]() Moiré SLs were also created in low-angle twisted graphene bilayers, followed by van der Waals structures made up of few layers of graphene 16, 17, 18, 19, 20, 21 and other 2D materials 22, 23. Periodic modulation has been obtained in graphene through chemical functionalization 7, placing graphene on self-assembled nanostructures 8, and by stacking graphene together with aligned or slightly misoriented hexagonal boron nitride (hBN), resulting in periodic moiré modulation which generates hexagonal superlattices (SLs) 9, 10, 11, 12, 13, 14, 15. Modifying the underlying graphene lattice by a smooth periodic potential can affect the band structure through folding of the pristine graphene Dirac cone into mini bands 1, formation of the secondary Dirac points, and anisotropic renormalization of velocity 2, 3, 4, 5, 6. Graphene, a 2D material characterized by a linear low-energy dispersion relation, hosts charge carriers named Dirac fermions due to the resemblance of relativistic (massless) particles described by the Dirac equation. Our quantum transport modeling provides an insight into the mini band structures, and can be applied to other superlattice geometries. At high magnetic field the calculated four-probe resistance fit the Hofstadter butterfly spectrum obtained for our superlattice. We find a good agreement between the focusing spectra and the mini band structures obtained from the continuum model, proving usefulness of this technique. We theoretically model transverse magnetic focusing, a ballistic transport technique by means of which we investigate the minibands, their extent and carrier type. At low magnetic field the dynamics of carriers reflects the semi-classical orbits which depend on the mini band structure. 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. Particularly interesting in this regard are superlattices with tunable modulation strength, such as electrostatically induced ones in graphene. In an external uniform magnetic field, a fractal energy spectrum called Hofstadter butterfly is formed. The presence of periodic modulation in graphene leads to a reconstruction of the band structure and formation of minibands. ![]()
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