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Register a new userLocal transport measurements at mesoscopic length scales using scanning tunneling potentiometry
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Under mesoscopic conditions, the transport potential on a thin film with current is theoretically expected to bear spatial variation due to quantum interference. Scanning tunneling potentiometry is the ideal tool to investigate such variation, by virtue of its high spatial resolution. We report in this {it Letter} the first detailed measurement of transport potential under mesoscopic conditions. Epitaxial graphene at a temperature of 17K was chosen as the initial system for study because the characteristic transport length scales in this material are relatively large. Tip jumping artifacts are a major possible contribution to systematic errors; and we mitigate such problems by using custom-made slender and sharp tips manufactured by focussed ion beam. In our data, we observe residual resistivity dipoles associated with topoographical defects, and local peaks and dips in the potential that are not associated with topographical defects.
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A theoretical description of scanning tunneling potentoimetry (STP) measurement is presented to address the increasing need for a basis to interpret experiments on macrscopic samples. Based on a heuristic understanding of STP provided to facilitate theoretical understanding, the total tunneling current related to the density matrix of the sample is derived within the general framework of quantum transport. The measured potentiometric voltage is determined implicitly as the voltage necessary to null the tunneling current. Explicit expressions of measured voltages are presented under certain assumptions, and limiting cases are discussed to connect to previous results. The need to go forward and formulate the theory in terms of a local density matrix is also discussed.
We study the relationship between the local density of states (LDOS) and the conductance variation $Delta G$ in scanning-gate-microscopy experiments on mesoscopic structures as a charged tip scans above the sample surface. We present an analytical model showing that in the linear-response regime the conductance shift $Delta G$ is proportional to the Hilbert transform of the LDOS and hence a generalized Kramers-Kronig relation holds between LDOS and $Delta G$. We analyze the physical conditions for the validity of this relationship both for one-dimensional and two-dimensional systems when several channels contribute to the transport. We focus on realistic Aharonov-Bohm rings including a random distribution of impurities and analyze the LDOS-$Delta G$ correspondence by means of exact numerical simulations, when localized states or semi-classical orbits characterize the wavefunction of the system.
We have constructed a scanning tunneling potentiometry system capable of simultaneously mapping the transport-related electrochemical potential of a biased sample along with its surface topography. Combining a novel sample biasing technique with a continuous current-nulling feedback scheme pushes the noise performance of the measurement to its fundamental limit - the Johnson noise of the STM tunnel junction. The resulting 130 nV voltage sensitivity allows us to spatially resolve local potentials at scales down to 2 nm, while maintaining angstrom scale STM imaging, all at scan sizes of up to 15 um. A mm-range two-dimensional coarse positioning stage and the ability to operate from liquid helium to room temperature with a fast turn-around time greatly expand the versatility of the instrument. By performing studies of several model systems, we discuss the implications of various types of surface morphology for potentiometric measurements.
We present scanning tunneling microscopy (STM) images of single-layer graphene crystals examined under ultrahigh vacuum conditions. The samples, with lateral dimensions on the micron scale, were prepared on a silicon dioxide surface by direct exfoliation of single crystal graphite. The single-layer films were identified using Raman spectroscopy. Topographic images of single-layer samples display the honeycomb structure expected for the full hexagonal symmetry of an isolated graphene monolayer. The absence of observable defects in the STM images is indicative of the high quality of these films. Crystals comprised of a few layers of graphene were also examined. They exhibited dramatically different STM topography, displaying the reduced three-fold symmetry characteristic of the surface of bulk graphite.
Growth of large-scale graphene is still accompanied by imperfections. By means of a four-tip STM/SEM the local structure of graphene grown on SiC(0001) was correlated with scanning electron microscope images and spatially resolved transport measurements. The systematic variation of probe spacings and substrate temperature has clearly revealed two-dimensional transport regimes of Anderson localization as well as of diffusive transport. The detailed analysis of the temperature dependent data demonstrates that the local on-top nano-sized contacts do not induce significant strain to the epitaxial graphene films.
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