Local breakdown of the quantum Hall effect in narrow single layer graphene Hall devices
Shortly after the discovery of the quantum Hall effect, the physical limits of this effect in various conditions such as sample mobility, temperature and bias current were widely investigated in two dimensional electron gas (2DEG) structures. The breakdown of the quantum Hall effect, which is observed as the abrupt increase in the longitudinal resistance with an associated loss in the quantization of Hall voltage is the major obstacle against improving the precision of the electrical resistance Standard. Although a comprehensive model that explains all the experimental results on the breakdown of quantum Hall effect does not exist, the proposed models provide insight to different aspects of the breakdown. Some of these models are intra and inter Landau-Level transitions,electron heating, impurity mediated tunneling and relaxation of the electrons and electron phonon interactions.
Graphene is inherently a 2D material and has an unusual band structure that allows the quantization of the Hall resistance even at room temperature. These unique properties of graphene make it a good candidate as a high precision metrological characterization tool for the quantum Hall resistance. The uncertainty in the quantum Hall resistance in graphene has been rapidly improving recently and graphene samples have already been shown to reach the precision of the current best 2DEG samples. In this talk, experimental results on the breakdown of the quantum Hall effect in graphene on SiOx will be presented. In narrow graphene samples of 1 micrometer width, the charge inhomogeneity is quite prominent and strongly affects the nondissipative transport in the quantum Hall regime. We have observed that the deviation of the Hall resistance from its quantized value is weakly dependent on the longitudinal resistivity up to current density of 5 A/m, where the Hall resistance remains quantized even when the longitudinal resistance increases monotonously with the current. Then a collapse in the quantized resistance occurs while longitudinal resistance keeps its gradual increase. The exponential increase of the conductivity with respect to the current suggests impurity mediated inter-Landau level scattering as the mechanism of the breakdown. The results are interpreted as the strong variation of the breakdown behavior throughout the sample due to the randomly distributed scattering centers that mediates the breakdown .
 C. Yanik, Ismet I. Kaya, e-print arXiv:1302.4729 ( In press, Solid State Communications)