Precision comparison of the quantum Hall effect in graphene and gallium arsenide

Abstract

The half-integer quantum Hall effect in epitaxial graphene is compared with\nhigh precision to the well known integer effect in a GaAs/AlGaAs\nheterostructure. We find no difference between the quantised resistance values\nwithin the relative standard uncertainty of our measurement of $8.7\\times\n10^{-11}$. The result places new tighter limits on any possible correction\nterms to the simple relation $R_{\\rm K}=h/e^2$, and also demonstrates that\nepitaxial graphene samples are suitable for application as electrical\nresistance standards of the highest metrological quality. We discuss the\ncharacterisation of the graphene sample used in this experiment and present the\ndetails of the cryogenic current comparator bridge and associated uncertainty\nbudget.\n