The heat kernel expansion for the electromagnetic field in a cavity

We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic Casimir energy is finite.Comment: 12 page

Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene

We present Raman spectroscopy measurements on single- and few-layer graphene flakes. Using a scanning confocal approach we collect spectral data with spatial resolution, which allows us to directly compare Raman images with scanning force micrographs. Single-layer graphene can be distinguished from double- and few-layer by the width of the D' line: the single peak for single-layer graphene splits into different peaks for the double-layer. These findings are explained using the double-resonant Raman model based on ab-initio calculations of the electronic structure and of the phonon dispersion. We investigate the D line intensity and find no defects within the flake. A finite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry

Quantum oscillations and a non-trivial Berry phase in the noncentrosymmetric superconductor BiPd

We report the measurements of de Haas-van Alphen (dHvA) oscillations in the noncentrosymmetric superconductor BiPd. Several pieces of a complex multi-sheet Fermi surface are identified, including a small pocket (frequency 40 T) which is three dimensional and anisotropic. From the temperature dependence of the amplitude of the oscillations, the cyclotron effective mass is ($0.18$ $\pm$ 0.1) $m_e$. Further analysis showed a non-trivial $\pi$-Berry phase is associated with the 40 T pocket, which strongly supports the presence of topological states in bulk BiPd and may result in topological superconductivity due to the proximity coupling to other bands.Comment: 5 pages, 3 figure

Raman imaging of doping domains in graphene on SiO2

We present spatially resolved Raman images of the G and 2D lines of single-layer graphene flakes. The spatial fluctuations of G and 2D lines are correlated and are thus shown to be affiliated with local doping domains. We investigate the position of the 2D line -- the most significant Raman peak to identify single-layer graphene -- as a function of charging up to |n|~4 10^12 cm^-2. Contrary to the G line which exhibits a strong and symmetric stiffening with respect to electron and hole-doping, the 2D line shows a weak and slightly asymmetric stiffening for low doping. Additionally, the line width of the 2D line is, in contrast to the G line, doping-independent making this quantity a reliable measure for identifying single-layer graphene

Tunable Coulomb blockade in nanostructured graphene

We report on Coulomb blockade and Coulomb diamond measurements on an etched, tunable single-layer graphene quantum dot. The device consisting of a graphene island connected via two narrow graphene constrictions is fully tunable by three lateral graphene gates. Coulomb blockade resonances are observed and from Coulomb diamond measurements a charging energy of ~3.5 meV is extracted. For increasing temperatures we detect a peak broadening and a transmission increase of the nanostructured graphene barriers

Coulomb oscillations in three-layer graphene nanostructures

We present transport measurements on a tunable three-layer graphene single electron transistor (SET). The device consists of an etched three-layer graphene flake with two narrow constrictions separating the island from source and drain contacts. Three lateral graphene gates are used to electrostatically tune the device. An individual three-layer graphene constriction has been investigated separately showing a transport gap near the charge neutrality point. The graphene tunneling barriers show a strongly nonmonotonic coupling as function of gate voltage indicating the presence of localized states in the constrictions. We show Coulomb oscillations and Coulomb diamond measurements proving the functionality of the graphene SET. A charging energy of $\approx 0.6$ meV is extracted.Comment: 10 pages, 6 figure

Local gating of a graphene Hall bar by graphene side gates

We have investigated the magnetotransport properties of a single-layer graphene Hall bar with additional graphene side gates. The side gating in the absence of a magnetic field can be modeled by considering two parallel conducting channels within the Hall bar. This results in an average penetration depth of the side gate created field of approx. 90 nm. The side gates are also effective in the quantum Hall regime, and allow to modify the longitudinal and Hall resistances