Integer and fractional quantum Hall effect in graphene heterostructure

The study of two-dimensional electron systems with extraordinarily low levels of disorder was, for a long time, the exclusive privilege of the epitaxial thin film research community. However, the successful isolation of graphene by mechanical exfoliation has truly disrupted this field. Furthermore, the assembly of heterostructures consisting of several layers of different 2D materials in arbitrary order by exploiting van der Waals forces has been a game-changer in the field of low-dimensional physics. This technique can be generalized to the large class of strictly 2D materials and offers unprecedented parameters to play with in order to tune electronic and other properties. It has led to a paradigm shift in the field of 2D condensed matter physics with bright prospects. In this review article, we discuss three device fabrication techniques towards high mobility devices: suspended structures, dry transfer, and pick-up transfer methods. We also address state-of-the-art device structures, which are fabricated by the van der Waals pick-up transfer method. Finally, we briefly introduce correlated ground states in the fractional quantum Hall regime.