An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimallythin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green’s functions represented as Sommerfeld integrals. The solution of plane-wave reflection and tran...

Two-dimensional optical materials, such as graphene, can be characterized by surface conductivity. So far, the transformation optics schemes have focused on three-dimensional properties such as permittivity ϵ and permeability μ. In this Letter, we use a scheme for transforming surface currents to highlight that the surface conductivity transforms in a way different from ϵ and μ. We use this sur...

For in situ measurements of local electrical conductivity of well defined crystal surfaces in ultrahigh vacuum, we have developed microscopic four-point probes with a probe spacing of several micrometres, installed in a scanningelectron-microscope/electron-diffraction chamber. The probe is precisely positioned on targeted areas of the sample surface by using piezoactuators. This apparatus enabl...

Nanochannel conductance measurements are commonly performed to characterize nanofluidic devices Theoretical analysis and experimental investigations imply that the nanochannel conductance does not follow the macro-scale models. It is generally accepted that the conductance of nanochannels deviates from the bulk and trend to a constant value at low concentrations. In this work, we present an imp...

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Four-point measurements using a multitip scanning tunneling microscope are carried out in order to determine surface and step conductivities on Si(111) surfaces. In a first step, distance-dependent four-point measurements in the linear configuration are used in combination with an analytical three-layer model for charge transport to disentangle the 2D surface conductivity from nonsurface contri...

In this paper we describe our investigations of the electrical conductivity of the silicon dioxide-air interface. It appears that this conductivity is caused by the adsorption of water vapour on the oxide surface and strongly depends on the relative humidity of the surrounding air. Considering this fact we have decided to investigate the possibility to reduce the surface conductivity by means o...

The surface conductivity of insulators in the field is usually very non-uniformly distributed. In this case the integral surface conductivity is not an appropriate parameter of pollution severity. A better evaluation can be achieved on the basis of local conductivity measurements by means of special probes, e.g. the rod probe or tissue strip probe. In this paper the form factors of different pr...