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. 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.

石墨烯中周期性调制的存在导致能带结构的重建和微带的形成。在外部均匀磁场中，形成称为霍夫施塔特蝴蝶的分形能谱。在这方面特别有趣的是具有可调调制强度的超晶格，例如石墨烯中的静电感应超晶格。我们在石墨烯中的栅极诱导方形二维超晶格中进行量子输运建模，并研究其与能带结构细节的关系。在低磁场下，载流子的动力学反映了取决于微型能带结构的半经典轨道。我们从理论上模拟了横向磁聚焦，这是一种弹道输运技术，通过它我们研究了微带、它们的范围和载体类型。我们发现聚焦光谱和从连续介质模型获得的微型能带结构之间有很好的一致性，证明了该技术的有用性。在高磁场下，计算出的四探针电阻符合为我们的超晶格获得的 Hofstadter 蝴蝶谱。我们的量子输运模型提供了对微型能带结构的深入了解，并且可以应用于其他超晶格几何形状。