Graphene nanoribbons will be essential components in future graphene nanoelectronics. However, in typical nanoribbons produced from lithographically patterned exfoliated graphene, the charge carriers travel only about ten nanometres between scattering events, resulting in minimum sheet resistances of about one kilohm per square. Here we show that 40-nanometre-wide graphene nanoribbons epitaxially grown on silicon carbide are single-channel room-temperature ballistic conductors on a length scale greater than ten micrometres, which is similar to the performance of metallic carbon nanotubes. This is equivalent to sheet resistances below 1 ohm per square, surpassing theoretical predictions for perfect graphene by at least an order of magnitude. In neutral graphene ribbons, we show that transport is dominated by two modes. One is ballistic and temperature independent; the other is thermally activated. Transport is protected from back-scattering, possibly reflecting ground-state properties of neutral graphene. At room temperature, the resistance of both modes is found to increase abruptly at a particular length--the ballistic mode at 16 micrometres and the other at 160 nanometres. Our epitaxial graphene nanoribbons will be important not only in fundamental science, but also--because they can be readily produced in thousands--in advanced nanoelectronics, which can make use of their room-temperature ballistic transport properties.

The electrical conductivity of solid-state matter is a fundamental physical property and can be precisely derived from the resistance measured via the four-point probe technique excluding contributions from parasitic contact resistances. Over time, this method has become an interdisciplinary characterization tool in materials science, semiconductor industries, geology, physics, etc, and is employed for both fundamental and application-driven research. However, the correct derivation of the conductivity is a demanding task which faces several difficulties, e.g. the homogeneity of the sample or the isotropy of the phases. In addition, these sample-specific characteristics are intimately related to technical constraints such as the probe geometry and size of the sample. In particular, the latter is of importance for nanostructures which can now be probed technically on very small length scales. On the occasion of the 100th anniversary of the four-point probe technique, introduced by Frank Wenner, in this review we revisit and discuss various correction factors which are mandatory for an accurate derivation of the resistivity from the measured resistance. Among others, sample thickness, dimensionality, anisotropy, and the relative size and geometry of the sample with respect to the contact assembly are considered. We are also able to derive the correction factors for 2D anisotropic systems on circular finite areas with variable probe spacings. All these aspects are illustrated by state-of-the-art experiments carried out using a four-tip STM/SEM system. We are aware that this review article can only cover some of the most important topics. Regarding further aspects, e.g. technical realizations, the influence of inhomogeneities or different transport regimes, etc, we refer to other review articles in this field.

Topological insulators are guaranteed to support metallic surface states on an insulating bulk, and one should thus expect that the electronic transport in these materials is dominated by the surfaces states. Alas, due to the high remaining bulk conductivity, surface contributions to transport have so-far only been singled out indirectly via quantum oscillations [1, 2], or for devices based on gated and doped topological insulator thin films, a situation in which the surface carrier mobility could be limited by defect and interface scattering [3][4][5][6]. Here we present the first direct measurement of surface-dominated conduction on an atomically clean surface of bulk-insulating Bi 2 Te 2 Se.Using nano-scale four point setups with variable contact distance, we show that the transport at 30 K is two-dimensional rather than three-dimensional and by combining these measurements with angle-resolved photoemission results from the same crystals, we find a surface state mobility of 390(30) cm 2 V −1 s −1 at 30 K at a carrier concentration of 8.71(7)×10 12 cm −2 .

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.

Adsorption of Au on vicinal Si(111) surfaces results in growth of long-range ordered metallic quantum wires. In this paper, we utilized site-specific and selective adsorption of oxygen to modify chemically the transport via different channels in the systems Si(553)-Au and Si(557)-Au. They were analyzed by electron diffraction and four-tip STM-based transport experiments. Modeling of the adsorption process by density functional theory shows that the adatoms and rest atoms on Si(557)-Au provide energetically favored adsorption sites, which predominantly alter the transport along the wire direction. Since this structural motif is missing on Si(553)-Au, the transport channels remain almost unaffected by oxidation.