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Electrical devices based on suspended multi-wall carbon nanotubes were constructed and studied. The chiral structure of each shell in a particular nanotube was determined using nanobeam electron diffraction in a transmission electron microscope. The transport properties of the carbon nanotube were also measured. The nanotube device length was short enough that the transport was nearly ballistic, and multiple subbands contributed to the conductance. Thermal excitation of carriers significantly affected nanotube resistance at room temperature.

A brief review of quantum interference in small conductors is followed by a discussion of quantum interference in ballistic conductors. The ballistic conductors are characterized by conservation of the momentum vector and this leads to a simple model for the details of the conductance of the system. In contrast, for diffusive conductors one can only predict the statistical behavior of the interference contributions to the conductance. The response of the ballistic interferometers is governed by semiclassical physics of the electron momentum states (i.e. the modes) in the quantum conductor. Under circumstances of reduced backscattering of the modes, the interference pattern appears to imitate that from a simple optical interferometer. New results from ballistic interferometers are reviewed briefly.

In GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As coupled four-ring and two-ring samples, large Aharonov-Bohm (AB) oscillations have been observed for magnetic fields 0B4.5 T. The oscillation spectrum changes systematically corresponding to the subband (Landau level) population inside the one-dimensional channels. Multiple tunneling between the edge states encircling the lithographically defined islands causes well-resolved high harmonics ne/h of the fundamental Aharonov-Bohm oscillation frequency with n\ensuremath{\le}8. Such high harmonics indicate participation from several islands and require very long phase coherence lengths ${\mathit{l}}_{\mathrm{\ensuremath{\varphi}}}$. The frequencies ${\mathit{f}}_{\mathit{n}}$=ne/h of all harmonics decrease with increasing B in accord with a simple model. These findings are evidence for ballistic transport in these large complex devices. The B dependence of the quantum interference amplitudes ${\mathit{G}}_{\mathit{n}}$(B) for AB oscillations of frequency ne/h is qualitatively different from the previously published results: They increase by about an order of magnitude with increasing B before decaying at very high field. The increase in ${\mathit{G}}_{\mathit{n}}$(B) is exploited to infer ${\mathit{l}}_{\mathrm{\ensuremath{\varphi}}}$ and indicates that ${\mathit{l}}_{\mathrm{\ensuremath{\varphi}}}$(B) increases with B at a rate \ensuremath{\ge}1.3 \ensuremath{\mu}m/T.

In a GaAs/AlGaAs 4-coupled-ring sample, large Aharonov-Bohm (AB) oscillations were studied up to harmonic order n = 8 for magnetic fields 0 < B < 4.5T. The frequencies of all harmonics of the AB oscillations decrease as predicted by a simple model. The results also suggest an increase of the quantum mechanical phase coherence length (lφ) with increased B.

We report measurements of the shear modulus of each shell and the friction between the two shells of double-shell carbon nanotubes in single nanotube-based nanoelectromechanical devices operated in a transmission electron microscope. In situ nanobeam electron diffraction is applied to obtain the chiral indices of each shell of the nanotube and it allows us to establish a quantitative correlation between the atomic structure and properties of the nanotube under investigation.

Tunnel junctions often have conductances that are linear in voltage over wide voltage ranges. Although this linear conductance background has received much attention recently in connection with the high-${\mathit{T}}_{\mathit{c}}$ superconductors, it is found in many systems. Previous work has shown that the discontinuity in slope of the linear conductance background at zero bias is thermally smeared by \ensuremath{\sim}5kT, consistent with inelastic tunneling from a broad, flat continuum of states. In this paper we concentrate on a particular system, junctions with ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ in the barrier region, in which the size of the effect can be adjusted by changing the barrier composition. Careful analysis of the Pb strong-coupling phonon structure in Al-${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$-Pb junctions is consistent with the inelastic-tunneling hypothesis, and inconsistent with a voltage-dependent matrix-element explanation for this effect. Suppression of the Al gap signature, as well as Zeeman splitting of the conductance background near zero bias, indicates that strong spin interactions occur in the barrier region in these junctions. We present Monte Carlo simulations of multiple-scattering strong inelastic tunneling to explain the very wide voltage range over which the linear background occurs. We argue that the same basic mechanism is probably responsible for the linear background in junctions involving high-${\mathit{T}}_{\mathit{c}}$ junctions as for the junctions studied in detail here.

The properties of a carbon nanotube (CNT), in particular a single-wall carbon nanotube (SWNT), are highly sensitive to the atomic structure of the nanotube described by its chirality (chiral indices). We have grown isolated SWNTs on a silicon substrate using chemical vapor deposition (CVD) and patterned sub-micron probes using electron beam lithography. The SWNT was exposed by etching the underlying substrate for transmission electron microscope (TEM) imaging and diffraction studies. For each individual SWNT, its electrical resistance was measured by the four-probe method at room temperature and the chiral indices of the same SWNT were determined by nano-beam electron diffraction. The contact resistances were reduced by annealing to typically 3-5 kΩ. We have measured the I-V curve and determined the chiral indices of each nanotube individually from four SWNTs selected randomly – two are metallic and two are semiconducting. We will present the electrical resistances in correlation with the carbon nanotube diameter as well as the band gap calculated from the determined chiral indices for the semiconducting carbon nanotubes. These experimental results are also discussed in connection with theoretical estimations.

We have fabricated a quantum dot with four leads attached via variable-width constrictions. At high magnetic fields and low temperatures, the h/2${\mathit{e}}^{2}$ and h/4${\mathit{e}}^{2}$ quantized Hall pleateaux observed for wide constrictions are replaced by a series of minima that go to zero or below as the constrictions are squeezed. These resonances are explained well by a recent model proposed by Kirczenow (following paper) to describe this structure, in which each lead transmits only one edge state. The minima can be explained by interference between edge states near the constrictions.

We present observations of resonance behavior in a torsional nanoelectromechanical device built with an individual single-walled carbon nanotube. The effect of applied torsional strain on the transport properties of the nanotube provides an electrical signal transducer and hence a means of measuring oscillation amplitude, resonance frequency, and quality factor. The mechanical resonance is confirmed by imaging and the electromechanical signal is compared to quasi-static measurements.

In narrow high-mobility conductors the predominant source of scattering is reflection of carriers off the confining potential. We demonstrate that by changing the geometry of the intersection of the Hall probes with the conductor, the Hall resistance can be quenched, negative or enhanced. More complex junction geometries can lead to one of these phenomena for one field polarity and to another for the other field polarity. At liquid helium temperatures these results can be explained by following trajectories. In the milli-Kelvin range fluctuations are superimposed. At high fields strong resonant depressions of the Hall resistance are found which may be associated with bound states in the region of the cross.

Conducting scanning probe microscopy provides a powerful tool for measuring electric transport through small surface features. In this chapter, carbon nanotubes and carbon nanotube networks are analyzed with a scanning probe microscopy method that employs solid metal tips to provide improved electrical contact to the nanotubes. The study reveals paths of electrical transport through carbon nanotubes and provides a means to differentiate between semiconducting and metallic nanotubes. Finally, high-resolution images provide insight into the conductance decay around nanotube junctions.

We have measured the decay of local conductance in single-wall carbon nanotubes directly using conductance imaging atomic force microscopy. The decay lengths were in the range from $190\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ to well over $3\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$. There are strong indications that these decay lengths are the result of depletion lengths around metallic/semiconducting carbon nanotube junctions, and that they are related to defects in the tubes.

We present local conductance measurements of carbon nanotube networks with nanometer scale resolution and show that there are discrete drops in conductance that correspond to junctions of metallic nanotubes and semiconducting nanotubes. The anomalies of these networks compared to thin films are shown, and a new method of discerning between semiconducting and metallic single-wall carbon nanotubes is demonstrated.

We discuss the mechanical properties of carbon nanotubes and devices incorporating carbon nanotubes. We demonstrate novel measurement and force application techniques using an atomic force microscope coupled to a unique computing environment that simplifies manipulations. We report on results from measurements of the mechanical and electronic interactions between nanotubes and graphite surfaces. We also fabricate nanometer‐scale electromechanical devices which incorporate nanotubes as springs, and discover a remarkable stiffening behavior of the nanotubes.

We have fabricated quantum devices from remotely doped Si/SiGe heterostructures. The devices are interferometers (loops) similar in plan to those used in experiments on ballistic GaAs/AlxGa1−xAs devices. The loops are approximately 2r=0.8 μm in diameter with linewidths of w=0.4 μm. We have observed clear Aharonov–Bohm (AB) oscillations that vanish systematically as the carrier temperature increases. Response of up to the second harmonic of the fundamental AB frequency e/h implies a phase coherence length of around Lφ=1.2 μm. In some samples, we see steps in conductance G(Vg) as a function of gate voltage similar to the ballistic mode steps seen in GaAs/AlxGa1−xAs point contacts.

We report on the characterization of torsional oscillators which use multi-walled carbon nanotubes as the spring elements. Through atomic-force-microscope force-distance measurements we are able to apply torsional strains to the nanotubes and measure their torsional spring constants and effective shear moduli. We find that the effective shear moduli cover a broad range, with the largest values near the theoretically predicted value. The data also suggest that the nanotubes are stiffened by repeated flexing., 4 pages

Studies of high mobility Si/SiGe heterostructure devices have been analyzed in light of correlations among carriers. Single-particle models fail to describe the metal-insulator transitions observed in them. Attempts to confine the carriers and create lateral tunneling structures and magnetic field sensors have revealed ambiguous results that cannot be distinguished from disorder in the devices but which show some promise for device applications.

Nanowires comprising a metal (Au) segment and a semiconductor segment (CdSe) were grown through an electrochemical process that allows the shape of the interface between the materials to be abrupt (planar) or to be tailored to form off-axis conical profiles. Polarized light was used to excite plasmons in the exposed end of the Au segment, and emission was studied at the Au:CdSe interface and at the distal end of the nanowire. Both the relative intensities of the emissions and the polarizations of the light from the distal end were correlated with the shapes of the interfaces. It was shown that the emission intensity and the degree of polarization were controlled by the interface shape. Finite difference time-domain studies of different interface shapes support the experimental conclusions.

The project to study quantum transport in Si/SiGe heterostructures has, in addition to attacking the proposed goals, emphasized work on the two-dimensional metal-insulator transition. Ballistic Aharonov-Bohm devices were made and studied. The experimental results on the metal-insulator complement and sharply contrast with the results from much lower mobility systems like Si-MOSFETs. Data can be scaled according to an equation drawn from considerations of zero-temperature quantum critical points, but with a much larger conductivity (by a factor of nearly 100) than in the more generic (lower) mobility samples.

We report low-temperature experiments on noise (in equilibrium and in the presence of current flow) in Hall bars with 0.5-\ensuremath{\mu}m gates across them. The Hall bars were formed on high-mobility GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructures, and by using the gate we were able to explore the noise characteristics both in the integer quantized Hall effect and for fractional filling factors. In the integer quantized Hall effect, the noise power exhibits plateaus where the resistance does, and it exhibits plateaus in spite of the lack of clear resistance plateaus when the filling factor is fractional beneath the gate. The excess noise found in the experiments is less than that predicted by the simple shot-noise formula.

A review of several experiments and techniques in the nanometer domain is given. The covered experiments and techniques are a sampling of the results obtained to date in the nanometer domain through an interdisciplinary collaboration that include computer scientists, materials scientists, social scientists and educators. The nano Manipulator provides a hands-on paradigm for materials science, biological science, educational methods and distance collaborations are being explored as well as providing a varied set of hard driving problems for computer science.

Coupled GaAs/GaAlAs rings have been fabricated using electron‐beam lithography and wet chemical etching. We report the first observation of conductance steps associated with e2/h in etched structures, and clear Aharonov–Bohm oscillations in multiple rings connected in parallel. The amplitude of the oscillations is found to be dependent on the number of rings indicating the possibility of phase coupling between electrons traversing different rings.

The Aharonov-Bohm effect in normal metal rings together with the associated conductance fluctuations in wires are clear signatures that experiments are now being performed in a quantum regime where conventional transport concepts do not apply. Ensemble averaging and taking the thermodynamic limit should not be used if comparisons to experiments are to be made. It is shown that by varying both the size of the sample as well as the temperature, we can study how ensemble averaging and energy averaging transforms a coherent quantum system into a classical one.

In mesoscopic metal films (size smaller than the inelastic diffusion length for the electrons), ensemble averaging is incomplete. Direct interference between the electron waves gives rise to a sample specific magnetoresistance. The magnetoresistance of a mesoscopic loop oscillates with flux-period h/e. In series arrays of mesoscopic loops, the h/e amplitude is inversely proportional to the square-root of the number of loops. This is in agreement with the stochastic "self-averaging" of the direct interference in larger samples. In long metal cylinders, impurity averaging is complete and only h/2e oscillations caused by the weak electron localization, are present.

Universal conductance fluctuations in wires and Aharonov-Bohm oscillations in loops are not symmetric about $H=0$. The observation of asymmetry in the periodic oscillations is possible when the phase-coherence length of the wave function is comparable to the separation of the voltage probes. In both cases, four-probe measurements yield resistances which depend on lead configuration. The asymmetries appear like Hall voltages, and are consistent with Onsager's relations.

Measurements of the magnetoresistance of very small Au rings have revealed Aharonov-Bohm oscillations with a fundamental period h/e . These oscillations persist to very large magnetic field. The temperature dependence of the oscillations is consistent with predictions that apply in the absence of inelastic scattering.

The magnetoresistance of small wires and loops is described. At low temperatures, the electrons retain quantum mechanical phase coherence for distances of a micron or so, which is the size scale over which the measurements are made. The random interference of the electron wavefunctions appears as random fluctuations in the magnetoresistance, and in loops, the Aharonov–Bohm effect causes periodic oscillations. The resistance varies randomly with the Fermi energy of the electrons, with the voltage across the sample, and with any transverse voltages applied by external gates. The nonlocal character of the wavefunction leads to resistance fluctuations in configurations where classical physics predicts null results. Throughout the discussion the physics is explained for those new to the field.

We report large logarithmic corrections to the conductivity of two-dimensional electrons and holes in GaSb-InAs-GaSb double heterostructures. From \ensuremath{\sim} 40 mK to 1 K, the conductivity increased with the logarithm of the temperature but with a slope as much as 30 times larger than estimated from the theories of weak localization and carrier interaction. The discrepancy apparently results from electron-hole interactions not included in the theory.

The averaging of Aharonov-Bohm oscillations caused by incomplete phase coherence has been studied in two Sb rings. In these devices, the phase-coherence length ${L}_{\ensuremath{\varphi}}$ can be determined independently from an analysis of the weak localization contribution to the magnetoconductance ($\ensuremath{\Delta}{G}_{C}$) or from the amplitude of the conductance fluctuations. We find that the Aharonov-Bohm oscillations decrease as $\mathrm{exp}(\ensuremath{-}\frac{L}{{L}_{\ensuremath{\varphi}}})$ where $L$ is the sample length. The values of ${L}_{\ensuremath{\varphi}}$ inferred from $\ensuremath{\Delta}{G}_{C}$ qualitatively predict the temperature dependence of the conductance fluctuations.

We report the temperature dependence of the Shubnikov-de Haas oscillations from a two-dimensional electron-hole system in GaSb-InAs-GaSb quantum wells at very low temperatures. The samples are double heterostructures containing separate electron and hole layers. The oscillations arising from the electron layer behave regularly with temperature. Additional oscillations, characterized by strong temperature dependence, and relatively large peak widths are believed to arise from the presence of hole layers. Keywords include: Magnetotransport, Two dimensional systems, InAs, GaSb, Heterostructures, and Quantum Hall Effect.

Measurements of the tunneling rate $\ensuremath{\Gamma}$ out of the zero-voltage state for several Nb edge junctions with differing shunt capacitances are described. At zero temperature, increasing the shunt capacitance lowers $\ensuremath{\Gamma}$ in agreement with dissipative calculations of the macroscopic-quantum-tunneling rate. As temperature increases, $\mathrm{ln}[\frac{\ensuremath{\Gamma}(T)}{\ensuremath{\Gamma}(0)}]\ensuremath{\propto}{T}^{2}$ as recently predicted.

We report measurements of the magneto and Hall resistance in GaSb-InAs-GaSb heterostructures at magnetic fields up to 28T and temperatures as low as 0.005K. In addition to the quantized Hall effect, extraordinary structures are observed, which cannot be accounted for in the framework of fractional Hall quantization present in one-carrier systems. These new features are attributed to the uniqueness of the InAs-GaSb system, where two-dimensional electrons and holes coexist.

Clear evidence of Aharonov–Bohm oscillations with respect to the flux quantum Φ0=h/e has been observed in the magnetoresistance of single, submicron diameter, normal metal rings. The rings were fabricated using contamination nanolithography in a personal computer controlled, high resolution, scanning transmission electron microscope. The magnetoresistance oscillations developed below T≂1 K, and, surprisingly, persisted without attenuation for more than 1000 periods.