A low-temperature dynamic mode scanning force microscope operating in high magnetic fields

A scanning force microscope was implemented operating at temperatures below 4.2K and in magnetic fields up to 8T. Piezoelectric quartz tuning forks were employed for non optical tip-sample distance control in the dynamic operation mode. Fast response was achieved by using a phase-locked loop for driving the mechanical oscillator. Possible applications of this setup for various scanning probe techniques are discussed.Comment: 5 pages, 5 figures, submitted to "Review of Scientific Instruments

Quantum capacitance and density of states of graphene

We report on measurements of the quantum capacitance in graphene as a function of charge carrier density. A resonant LC-circuit giving high sensitivity to small capacitance changes is employed. The density of states, which is directly proportional to the quantum capacitance, is found to be significantly larger than zero at and around the charge neutrality point. This finding is interpreted to be a result of potential fluctuations with amplitudes of the order of 100 meV in good agreement with scanning single-electron transistor measurements on bulk graphene and transport studies on nanoribbons

Local oxidation of Ga[Al]As heterostructures with modulated tip-sample voltages

Nanolithography based on local oxidation with a scanning force microscope has been performed on an undoped GaAs wafer and a Ga[Al]As heterostructure with an undoped GaAs cap layer and a shallow two-dimensional electron gas. The oxide growth and the resulting electronic properties of the patterned structures are compared for constant and modulated voltage applied to the conductive tip of the scanning force microscope. All the lithography has been performed in non-contact mode. Modulating the applied voltage enhances the aspect ratio of the oxide lines, which significantly strengthens the insulating properties of the lines on GaAs. In addition, the oxidation process is found to be more reliable and reproducible. Using this technique, a quantum point contact and a quantum wire have been defined and the electronic stability, the confinement potential and the electrical tunability are demonstrated to be similar to the oxidation with constant voltage.Comment: 7 pages, 7 figures, accepted by J. Appl. Phy

Operation characteristics of piezoelectric quartz tuning forks in high magnetic fields at liquid helium temperatures

Piezoelectric quartz tuning forks are investigated in view of their use as force sensors in dynamic mode scanning probe microscopy at temperatures down to 1.5 K and in magnetic fields up to 8 T. The mechanical properties of the forks are extracted from the frequency dependent admittance and simultaneous interferometric measurements. The performance of the forks in a cryogenic environment is investigated. Force-distance studies performed with these sensors at low temperatures are presented

Counting statistics and super-Poissonian noise in a quantum dot

We present time-resolved measurements of electron transport through a quantum dot. The measurements were performed using a nearby quantum point contact as a charge detector. The rates for tunneling through the two barriers connecting the dot to source and drain contacts could be determined individually. In the high bias regime, the method was used to probe excited states of the dot. Furthermore, we have detected bunching of electrons, leading to super-Poissonian noise. We have used the framework of the full counting statistics (FCS) to model the experimental data. The existence of super-Poissonian noise suggests a long relaxation time for the involved excited state, which could be related to the spin relaxation time

An Integrand Reconstruction Method for Three-Loop Amplitudes

We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Groebner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.Comment: 15 pages, 1 figur

Quantum capacitance and density of states of graphene

Abstract We report capacitance measurements in top-gated graphene sheets as a function of charge carrier density. A measurement method using an LC-circuit provides high sensitivity to small capacitance changes and hence allows the observation of the quantum part of the capacitance. The extracted density of states has a finite value of 1 × 10 17 m −2 eV −1 in the vicinity of the Dirac point, which is in contrast to the theoretical prediction for ideal graphene. We attribute this discrepancy to fluctuations of the electrostatic potential with a typical amplitude of 100 meV in our device

A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower argued that the reduction to master integrals is complicated by the presence of integrals with doubled propagator denominators in the integration by parts relations and they introduced a novel reduction procedure which eliminates all such integrals from the start. Their approach has the advantage that it automatically produces integral bases which mesh well with generalized unitarity. The heart of their procedure is an algorithm which utilizes the weighty machinery of computational commutative algebra to produce complete sets of unitarity-compatible integration by parts relations. In this paper, we propose a conceptually simpler algorithm for the generation of complete sets of unitarity-compatible integration by parts relations based on recent results in the mathematical literature. A striking feature of our algorithm is that it can be described entirely in terms of straightforward linear algebra.Comment: 20 pages; My apologies to Krzysztof Kajda for misspelling his name in v1; in v3: the labeling of the variables in (4.5) and eqs. (4.20) and (4.21) was adjusted to match the notation used in the rest of Section 4. I thank York Schroeder for pointing out the notational inconsistenc