Undoped diamond, a remarkable bulk electrical insulator, exhibits a high surface conductivity in air when the surface is hydrogen-terminated. Although theoretical models have claimed that a two-dimensional hole gas is established as a result of surfa
ce energy band bending, no definitive experimental demonstration has been reported so far. Here, we prove the two-dimensional character of the surface conductivity by low temperature characterization of diamond in-plane gated field-effect transistors that enable the lateral confinement of the transistors drain-source channel to nanometer dimensions. In these devices, we observe Coulomb blockade effects of multiple quantum islands varying in size with the gate voltage. The charging energy and thus the size of these zero-dimensional islands exhibits a gate voltage dependence which is the direct result of the two-dimensional character of the conductive channel formed at hydrogen-terminated diamond surfaces.
To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the lowest-or
der statistic providing an estimate for non-Gaussianities of a distribution, and the bispectrum covariance depicts the errors of the bispectrum measurement and their correlation on different scales. Currently, there do exist fitting formulae for the bispectrum and an analytical expression for the bispectrum covariance, but the former is not very accurate and the latter contains several intricate terms and only one of them can be readily evaluated from the power spectrum of the studied field. Neglecting all higher-order terms results in the Gaussian approximation of the bispectrum covariance. We study the range of validity of this Gaussian approximation for two-dimensional non-Gaussian random fields. For this purpose, we simulate Gaussian and non-Gaussian random fields, the latter represented by log-normal fields and obtained directly from the former by a simple transformation. From the simulated fields, we calculate the power spectra, the bispectra, and the covariance from the sample variance of the bispectra, for different degrees of non-Gaussianity alpha, which is equivalent to the skewness on a given angular scale theta g. We find that the Gaussian approximation provides a good approximation for alpha<0.6 and a reasonably accurate approximation for alpha< 1, both on scales >8theta g. Using results from cosmic shear simulations, we estimate that the cosmic shear convergence fields are described by alpha<0.7 at theta g~4. We therefore conclude that the Gaussian approximation for the bispectrum covariance is likely to be applicable in ongoing and future cosmic shear studies.
