Quantum transport in graphene Hall bars: Effects of vacancy disorder

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Using the tight-binding model, we investigate the influence of vacancy disorder on electrical transport in graphene Hall bars in the presence of quantizing magnetic fields. Disorder, induced by a random distribution of monovacancies, breaks the graphene sublattice symmetry and creates states localized on the vacancies. These states are observable in the bend resistance, as well as in the total DOS. Their energy is proportional to the square root of the magnetic field, while their localization length is proportional to the cyclotron radius. At the energies of these localized states, the electron current flows around the monovacancies and, as we show, it can follow unexpected paths depending on the particular arrangement of vacancies. We study how these localized states change with the vacancy concentration, and what are the effects of including the next nearest neighbor hopping term. Our results are also compared with the situation when double vacancies are present in the system. Double vacancies also induce localized states, but their energy and magnetic field dependences are different. Their localization energy scales linearly with the magnetic field, and their localization length appears not to depend on the field strength.