Paul Leonardus de Boeij

Optical anisotropy of Ge(001)2x1

We have measured the change in the optical reflection anisotropy of a clean Ge(001) surface upon exposure to molecular oxygen up to saturation coverage. Both phase and amplitude changes have been recorded with a normal-incidence ellipsometer. They have been found to be related by a Kramers-Kronig transformation. The change in the complex reflection ratio could be interpreted as an anisotropy of the clean Ge(001)2 × 1 surface dielectric function, using a three-layer McIntyre-Aspnes approach and neglecting the oxygen overlayer. The surface dielectric function anisotropy can be described fairly well by optical selection rules, based on symmetry arguments. This model was applied to the possible optical transitions at this surface between filled dimers, dangling bonds and back-bonds and the empty dangling bonds and dimers.

Gauge-Invariant Formulation of Circular Dichroism

Standard formulations of magnetic response properties, such as circular dichroism spectra, are plagued by gauge dependencies, which can lead to unphysical results. In this work, we present a general gauge-invariant and numerically efficient approach for the calculation of circular dichroism spectra from the current density. First we show that in this formulation the optical rotation tensor, the response function from which circular dichroism spectra can be obtained, is independent of the origin of the coordinate system. We then demonstrate that its trace is independent of the gauge origin of the vector potential. We also show how gauge invariance can be retained in practical calculations with finite basis sets. As an example, we explain how our method can be applied to time-dependent current-density-functional theory. Finally, we report gauge-invariant circular dichroism spectra obtained using the adiabatic local-density approximation. The circular dichroism spectra we thus obtain are in good agreement with experiment.

Spatially resolved electronic structure of twisted graphene

We have used scanning tunneling microscopy and spectroscopy to resolve the spatial variation of the density of states of twisted graphene layers on top of a highly oriented pyrolytic graphite substrate. Owing to the twist a moire pattern develops with a periodicity that is substantially larger than the periodicity of a single layer graphene. The twisted graphene layer has electronic properties that are distinctly different from that of a single layer graphene due to the nonzero interlayer coupling. For small twist angles (∼1-3.5) the integrated differential conductivity spectrum exhibits two well-defined Van Hove singularities. Spatial maps of the differential conductivity that are recorded at energies near the Fermi level exhibit a honeycomb structure that is comprised of two inequivalent hexagonal sublattices. For energies |E-EF|>0.3eV the hexagonal structure in the differential conductivity maps vanishes. We have performed tight-binding calculations of the twisted graphene system using the propagation method, in which a third graphene layer is added to mimic the substrate. This third layer lowers the symmetry and explains the development of the two hexagonal sublattices in the moire pattern. Our experimental results are in excellent agreement with the tight-binding calculations.