Person:

Westervelt, Robert

Graphene provides a fascinating testbed for new physics and exciting opportunities for future applications based on quantum phenomena. To understand the coherent flow of electrons through a graphene device, we employ a nanoscale probe that can access the relevant length scales—the tip of a liquid-He-cooled scanning probe microscope (SPM) capacitively couples to the graphene device below, creating a movable scatterer for electron waves. At sufficiently low temperatures and small size scales, the diffusive transport of electrons through graphene becomes coherent, leading to universal conductance fluctuations (UCF). By scanning the tip over a device, we map these conductance fluctuations versus scatterer position. We find that the conductance is highly sensitive to the tip position, producing (\delta G \sim e^2/h) fluctuations when the tip is displaced by a distance comparable to half the Fermi wavelength. These measurements are in good agreement with detailed quantum simulations of the imaging experiment and demonstrate the value of a cooled SPM for probing coherent transport in graphene.

The aggregation of superparamagnetic iron oxide (SPIO) nanoparticles decreases the transverse nuclear magnetic resonance (NMR) relaxation time (T_{2}^{CP}) of adjacent water molecules measured by a Carr-Purcell-Meiboom-Gill (CPMG) pulse-echo sequence. This effect is commonly used to measure the concentrations of a variety of small molecules. We perform extensive Monte Carlo simulations of water diffusing around SPIO nanoparticle aggregates to determine the relationship between (T_{2}^{CP}) and details of the aggregate. We find that in the motional averaging regime (T_{2}^{CP}) scales as a power law with the number (N) of nanoparticles in an aggregate. The specific scaling is dependent on the fractal dimension (d) of the aggregates. We find (T_{2}^{CP} \propto N^{-0.44}) for aggregates with (d=2.2), a value typical of diffusion limited aggregation. We also find that in two-nanoparticle systems, (T_{2}^{CP}) is strongly dependent on the orientation of the two nanoparticles relative to the external magnetic field, which implies that it may be possible to sense the orientation of a two-nanoparticle aggregate. To optimize the sensitivity of SPIO nanoparticle sensors, we propose that it is best to have aggregates with few nanoparticles, close together, measured with long pulse-echo times.

Graphene has opened new avenues of research in quantum transport, with potential applications for coherent electronics. Coherent transport depends sensitively on scattering from microscopic disorder present in graphene samples: electron waves traveling along different paths interfere, changing the total conductance. Weak localization is produced by the coherent backscattering of waves, while universal conductance fluctuations are created by summing over all paths. In this work, we obtain conductance images of weak localization with a liquid-He-cooled scanning probe microscope, by using the tip to create a movable scatterer in a graphene device. This technique allows us to investigate coherent transport with a probe of size comparable to the electron wavelength. Images of magnetoconductance versus tip position map the effects of disorder by moving a single scatterer, revealing how electron interference is modified by the tip perturbation. The weak localization dip in conductivity at (B=0) is obtained by averaging magnetoconductance traces at different positions of the tip-created scatterer. The width (\Delta B_{WL}) of the dip yields an estimate of the electron coherence length (L_{\phi}) fixed charge density. This 'scanning scatterer' method provides a new way of investigating coherent transport in graphene by directly perturbing the disorder configuration that creates these interferometric effects.

We study conductance fluctuations (CF) and the sensitivity of the conductance to the motion of a single scatterer in two-dimensional massless Dirac systems. Our extensive numerical study finds limits to the predicted universal value of CF. We find that CF are suppressed for ballistic systems near the Dirac point and approach the universal value at sufficiently strong disorder. The conductance of massless Dirac fermions is sensitive to the motion of a single scatterer. CF of order e2/h result from the motion of a single impurity by a distance comparable to the Fermi wavelength. This result applies to graphene systems with a broad range of impurity strength and concentration while the dependence on the Fermi wavelength can be explored via gate voltages. Our prediction can be tested by comparing graphene samples with varying amounts of disorder and can be used to understand interference effects in mesoscopic graphene devices.

We demonstrate atomic force microscope(AFM) imaging using dielectrophoresis(DEP) with coaxial probes. DEP provides force contrast allowing coaxial probes to image with enhanced spatial resolution. We model a coaxial probe as an electric dipole to provide analytic formulas for DEP between a dipole, dielectric spheres, and a dielectric substrate. AFM images taken of dielectric spheres with and without an applied electric field show the disappearance of artifacts when imaging with DEP. Quantitative agreement between our model and experiment shows that we are imaging with DEP.