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Phase space for the breakdown of the quantum Hall effect in epitaxial graphene

The quantum Hall effect in two – dimensional electron gases is characterised by a vanishing longitudinal resistivity and a quantised Hall resistance ρxy=h/νe2 for integer ν. The Hall resistance, determined by Planck’s constant h and the charge of an electron e, is used as a quantum standard to which all other electrical resistances can be accurately compared. The limiting factor for the accuracy is determined by the maximum current the Hall bar can carry whilst maintaining the quantum Hall state. At present the quantum resistance standard is based on GaAs/AlGaAs heterostructures which require very low temperatures (300mK) and high magnetic fields to observe an accurate quantum Hall effect, restricting their use to all but the most specialist metrology labs. Recently, researchers at the University of Oxford and LNCMI – Grenoble, in collaboration with the UK National Physical Laboratory, have shown that graphene grown epitaxially on the Si-terminated face of SiC is the ideal candidate for a quantum electrical resistance standard where the quantum Hall state is maintained at current densities over an order of magnitude larger than those in GaAs (Fig. 1a) [1]. In addition, the facilities of the LNCMI – Grenoble allowed the researchers to study the temperature dependence of this maximum current density, revealing that the dissipationless quantum Hall state can persist above 40 K (Fig. 1b). This work is now being used to develop low – cost, graphene – based, quantum resistance standards capable of operating at higher temperatures and lower magnetic fields.

Fig. 1: a) Magnetotransport and I-V data. The hatched region represents the dissipationless quantum Hall state which we observe to current densities of over 40 A/m. b) Magnetic field dependence of critical temperature, Tc, showing an approximately B2 behaviour.

 

[1] JA Alexander-Webber, AMR Baker, TJBM Janssen, A Tzalenchuk, S Lara-Avila, S Kubatkin, R Yakimova, BA Piot, DK Maude, and RJ Nicholas. Phase space for the breakdown of the quantum Hall effect in epitaxial graphene, Physical Review Letters 111, 096601 (2013).