The quantum Hall effect allows the international standard for resistance to be defined in terms of the electron charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of R(K) = h/e(2) = 25,812.807557(18) Omega, 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. Graphene should, in principle, be an ideal material for a quantum resistance standard, because it is inherently two-dimensional and its discrete electron energy levels in a magnetic field (the Landau levels) are widely spaced. However, the precisions demonstrated so far have been lower than one part per million. Here, we report a quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene at 300 mK, four orders of magnitude better than previously reported. Moreover, by demonstrating the structural integrity and uniformity of graphene over hundreds of micrometres, as well as reproducible mobility and carrier concentrations across a half-centimetre wafer, these results boost the prospects of using epitaxial graphene in applications beyond quantum metrology.

The performance of a great variety of electronic devices-ranging from semiconductor transistors to superconducting qubits-is hampered by low-frequency noise with spectra proportional to 1/f. The ubiquity and negative impact of 1/f noise has motivated intensive research into its cause, and it is now believed to originate from a bath of fluctuating two-level defect states (TLSs) embedded in the material. This phenomenon is commonly described by the long-established standard tunnelling model (STM) of independent TLS. A key prediction of STM is that the noise should vanish at low temperatures. Here we report measurements on superconducting microresonators over previously unattainable, very long time scales that show an increase in 1/f noise at low temperatures and low microwave power, contrary to the STM. We propose a new generalised tunnelling model that includes significant interaction between multiple TLSs, which fully describes these observations, as well as recent studies of individual TLS lifetimes in superconducting qubits.

We compare the three most commonly used scanning probe techniques to obtain a reliable value of the work function in graphene domains of different thickness. The surface potential (SP) of graphene is directly measured in Hall bar geometry via a combination of electrical functional microscopy and spectroscopy techniques, which enables calibrated work function measurements of graphene domains in ambient conditions with values Φ1LG ~4.55 ± 0.02 eV and Φ2LG ~ 4.44 ± 0.02 eV for single- and bi-layer, respectively. We demonstrate that frequency-modulated Kelvin probe force microscopy (FM-KPFM) provides more accurate measurement of the SP than amplitude-modulated (AM)-KPFM. The discrepancy between experimental results obtained by different techniques is discussed. In addition, we use FM-KPFM for contactless measurements of the specific components of the device resistance. We show a strong non-Ohmic behavior of the electrode-graphene contact resistance and extract the graphene channel resistivity.