Graphene and the universality of the quantum Hall effect

The quantum Hall effect allows the standard for resistance to be defined in terms of the elementary charge and Planck's constant alone. The effect-comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of RK = h/e(2) = 25 812.807 443 4 (84) Omega (Mohr P. J. et al., Rev. Mod. Phys., 84 (2012) 1527), the resistance quantum. Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology, a few parts per billion, has been achieved only in silicon and III-V heterostructure devices. In this lecture we show that graphene - a single layer of carbon atoms - beats these well-established semiconductor materials as the system of choice for the realisation of the quantum resistance standard. Here we shall briefly describe graphene technology, discuss the structure and electronic properties of graphene, including the unconventional quantum Hall effect and then present in detail the route, which led to the most precise quantum Hall resistance universality test ever performed.