Hopping magnetoresistance in strongly disordered monolayer graphene

Magnetoresistance (MR) of ion irradiated monolayer graphene samples with variable-range hopping (VRH) mechanism of conductivity was measured at temperatures down to T = 1.8 K in perpendicular and parallel magnetic fields up to B = 8 T. It is shown that in perpendicular magnetic fields, conductivity increases, or negative MR (NMR) is observed, while parallel magnetic field results in positive MR (PMR) at low temperatures. NMR is explained on the basis of the orbital model in which magnetic field suppresses the destructive interference of many paths through the intermediate sites in the total probability of the long-distance tunneling in the VRH regime. Samples with different degree of disorder were studied systematically. It is found that all NMR curves for different samples and different temperatures are merged into one common curve when plotted as a function of B/B*, where B* is experimentally determined magnetic field at which the quadratic dependence of NMR on B is replaced by the linear one. It is shown that B*~ T^{1/2} in agreement with theoretical predictions. The obtained values of B* allowed to determine the localization radius {\xi} for different samples. It is shown that {\xi} decreases expectedly with increase of disorder. PMR in parallel magnetic fields is explained by the alignment of electron spins which results in suppression of hopping transitions via double occupied states.