Extraordinary magnetoresistance in encapsulated monolayer graphene

We report a study on the phenomenon of extraordinary magnetoresistance (EMR) in boron nitride encapsulated monolayer graphene devices. Each device is circular, with an internal circular metal shunt made by edge contact to the graphene. Extremely large EMR values--calculated as (R(B) - R0) / R0, can be found in these devices due to the vanishingly small resistance values at zero field. In many devices the zero-field resistance can become negative, likely due to ballistic carrier transport. This enables R0 to be chosen arbitrarily close to zero depending only on measurement precision, resulting in very large EMR; conversely, small values of R0 can have large uncertainty in short term measurements, leading to very large error bars on the EMR. We critically discuss the dependence of EMR on measurement precision and device asymmetry. Finally, the gate-voltage-dependent resistance at zero field also shows a strong electron-hole asymmetry, which we trace to the nature of the metal-graphene edge contact: as in the well-studied case of metals deposited on graphene, the graphene at one-dimensional edge contacts also appears to be heavily electron-doped ~100s of nm away from the contact. We also report the effects of the sizes of the devices and the ratios of metal shunt to graphene on EMR.