Imaging coherent transport in graphene (Part II): Probing weak localization

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 \textit{vs.} 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 $L_\phi$ at 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.Comment: 18 pages, 7 figure

Triaxial AFM Probes for Noncontact Trapping and Manipulation

We show that a triaxial atomic force microscopy probe creates a noncontact trap for a single particle in a fluid via negative dielectrophoresis. A zero in the electric field profile traps the particle above the probe surface, avoiding adhesion, and the repulsive region surrounding the zero pushes other particles away, preventing clustering. Triaxial probes are promising for three-dimensional assembly and for selective imaging of a particular property of a sample using interchangeable functionalized particles.Engineering and Applied Science

Proposed Triaxial Atomic Force Microscope Contact Free Tweezers for Nanoassembly

We propose a triaxial atomic force microscope contact-free tweezer (TACT) for the controlled assembly of nanoparticles suspended in a liquid. The TACT overcomes four major challenges faced in nanoassembly, as follows. (1) The TACT can hold and position a single nanoparticle with spatial accuracy smaller than the nanoparticle size (~5 nm). (2) The nanoparticle is held away from the surface of the TACT by negative dielectrophoresis to prevent van der Waals forces from making it stick to the TACT. (3) The TACT holds nanoparticles in a trap that is size-matched to the particle and surrounded by a repulsive region so that it will only trap a single particle at a time. (4) The trap can hold a semiconductor nanoparticle in water with a trapping energy greater than the thermal energy. For example, a 5 nm radius silicon nanoparticle is held with 10 kBT at room temperature. We propose methods for using the TACT as a nanoscale pick-and-place tool to assemble semiconductor quantum dots, biological molecules, semiconductor nanowires, and carbon nanotubes.Engineering and Applied Science

Extracting the Density Profile of an Electronic Wave Function in a Quantum Dot

We use a model of a one-dimensional nanowire quantum dot to demonstrate the feasibility of a scanning probe microscope (SPM) imaging technique that can extract both the energy of an electron state and the amplitude of its wave function using a single instrument. This imaging technique can probe electrons that are buried beneath the surface of a low-dimensional semiconductor structure and provide valuable information for the design of quantum devices. A conducting SPM tip, acting as a movable gate, measures the energy of an electron state using Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wave function $\Psi(x)$ of the quantum state, changing the electron's energy by an amount proportional to $\mid\Psi(x)\mid^2$. By recording the change in energy as the SPM tip is moved along the length of the dot, the density profile of the electronic wave function can be found along the length of the quantum dot.Engineering and Applied Science

Coaxial atomic force microscope probes for imaging with dielectrophoresis

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.Engineering and Applied Science

Automating Microfluidics: Reconfigurable Virtual Channels for Cell and Droplet Transport

The emerging field of digital microfluidics promises to solve many shortcomings of traditional continuous-flow fluidics. This technology has a few incarnations, including EWOD (eletrowetting on dielectric) and DEP (dielectrophoresis) chips. Both consist of large arrays of electrical pixels which move droplets and cells. They actuate fluids actively, have error feedback, are programmable, perform operations in parallel, and do not rely on external pumps. For these reasons we foresee the increased use of digital microfluidics in the near future. We also foresee a gradual shift away from purpose-built microfluidic devices, towards multi-purpose platforms with specific applications encoded in software. To this extent we present here a new paradigm of encoding and automating microfluidic operations using video files. We use this technology to create several configurations of virtual microfluidic channels and to play film clips using living cells on a DEP chip.Engineering and Applied SciencesPhysic

Microwave Dielectric Heating of Drops in Microfluidic Devices

We present a technique to locally and rapidly heat water drops in microfluidic devices with microwave dielectric heating. Water absorbs microwave power more efficiently than polymers, glass, and oils due to its permanent molecular dipole moment that has a large dielectric loss at GHz frequencies. The relevant heat capacity of the system is a single thermally isolated picoliter drop of water and this enables very fast thermal cycling. We demonstrate microwave dielectric heating in a microfluidic device that integrates a flow-focusing drop maker, drop splitters, and metal electrodes to locally deliver microwave power from an inexpensive, commercially available 3.0 GHz source and amplifier. The temperature of the drops is measured by observing the temperature dependent fluorescence intensity of cadmium selenide nanocrystals suspended in the water drops. We demonstrate characteristic heating times as short as 15 ms to steady-state temperatures as large as 30 degrees C above the base temperature of the microfluidic device. Many common biological and chemical applications require rapid and local control of temperature, such as PCR amplification of DNA, and can benefit from this new technique.Comment: 6 pages, 4 figure