The conductance of multiwalled carbon nanotubes (MWNTs) was found to be quantized. The experimental method involved measuring the conductance of nanotubes by replacing the tip of a scanning probe microscope with a nanotube fiber, which could be lowered into a liquid metal to establish a gentle electrical contact with a nanotube at the tip of the fiber. The conductance of arc-produced MWNTs is one unit of the conductance quantum G0 5 2e 2 /h 5 (12.9 kilohms) ‐1 . The nanotubes conduct current ballistically and do not dissipate heat. The nanotubes, which are typically 15 nanometers wide and 4 micrometers long, are several orders of magnitude greater in size and stability than other typical room-temperature quantum conductors. Extremely high stable current densities, J . 10 7 amperes per square centimeter, have been attained.

http://www.nanoscience.gatech.edu/zlwang/paper/1998/98_sci_1.pdf

Carbon nanotube quantum resistors

Quantification of biological or biochemical processes are of utmost importance for medical, biological and biotechnological applications. However, converting the biological information to an easily processed electronic signal is challenging due to the complexity of connecting an electronic device directly to a biological environment. Electrochemical biosensors provide an attractive means to analyze the content of a biological sample due to the direct conversion of a biological event to an electronic signal. Over the past decades several sensing concepts and related devices have been developed. In this review, the most common traditional techniques, such as cyclic voltammetry, chronoamperometry, chronopotentiometry, impedance spectroscopy, and various field-effect transistor based methods are presented along with selected promising novel approaches, such as nanowire or magnetic nanoparticle-based biosensing. Additional measurement techniques, which have been shown useful in combination with electrochemical detection, are also summarized, such as the electrochemical versions of surface plasmon resonance, optical waveguide lightmode spectroscopy, ellipsometry, quartz crystal microbalance, and scanning probe microscopy. The signal transduction and the general performance of electrochemical sensors are often determined by the surface architectures that connect the sensing element to the biological sample at the nanometer scale. The most common surface modification techniques, the various electrochemical transduction mechanisms, and the choice of the recognition receptor molecules all influence the ultimate sensitivity of the sensor. New nanotechnology-based approaches, such as the use of engineered ion-channels in lipid bilayers, the encapsulation of enzymes into vesicles, polymersomes, or polyelectrolyte capsules provide additional possibilities for signal amplification. In particular, this review highlights the importance of the precise control over the delicate interplay between surface nano-architectures, surface functionalization and the chosen sensor transducer principle, as well as the usefulness of complementary characterization tools to interpret and to optimize the sensor response.

/pdf/electrochemical-biosensors-sensor-principles-and-5i1lr0kwi6.pdf

Electrochemical Biosensors - Sensor Principles and Architectures

I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). 
II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). 
III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). 
IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

/pdf/quantum-transport-in-semiconductor-nanostructures-1n3dkljf6x.pdf

Quantum Transport in Semiconductor Nanostructures

Publisher Summary Quantum transport is conveniently studied in a two-dimensional electron gas (2DEG) because of the combination of a large Fermi wavelength and large mean free path. Semiconductor nanostructures are unique in offering the possibility of studying quantum transport in an artificial potential landscape. This is the regime of ballistic transport in which scattering with impurities are neglected. The chapter presents a self-contained account of these three novel transport regimes in semiconductor nanostructures. The study of quantum transport in semiconductor nanostructures is motivated by more than scientific interest. The fabrication of nanostructures relies on sophisticated crystal growth and lithographic techniques that exist because of the industrial effort toward the miniaturization of transistors. Conventional transistors operate in the regime of classical diffusive transport, which breaks down on short length scales. The discovery of novel transport regimes in semiconductor nanostructures provides options for the development of innovative future devices.

/pdf/quantum-transport-in-semiconductor-nanostructures-3vpunw3uta.pdf

Early quantum theories of electrical conduction were semiclassical. Electrons were accelerated according to Bloch’s theorem; this was balanced by back scattering due to phonons and lattice defects. Cross sections for scattering, and band structures, were calculated quantum-mechanically, but the balancing process allowed only for occupation probabilities, not permitting a totally coherent process. Also, in most instances, scatterers at separate locations were presumed to act incoherently. Totally quantum-mechanical theories stem from the 1950s, and have diverse sources. Particularly intense concern with the need for more quantum mechanical approaches was manifested in Japan, and Kubo’s formulation became the most widely accepted version. Quantum theory, as described by the Schrodinger equation, is a theory of conservative systems, and does not allow for dissipation. The Schrodinger equation readily allows us to calculate polarizability for atoms, molecules, or other isolated systems that do not permit electrons to enter or leave. Kubo’s linear-response theory is essentially an extended theory of polarizability. Some supplementary handwaving is needed to calculate a dissipative effect such as conductance, for a sample with boundaries where electrons enter and leave (Anderson, 1997). After all, no theory that ignores the interfaces of a sample to the rest of its circuit can possibly calculate the resistance of such a sample of limited extent. Modern microelectronics has provided the techniques for fabricating very small samples. These permit us to study conductance in cases where the carriers have a totally quantum mechanically coherent history within the sample, making it essential to take the interfaces into account. Mesoscopic physics, concerned with samples that are intermediate in size between the atomic scale and the macroscopic one, can now demonstrate in manufactured structures much of the quantum mechanics we associate with atoms and molecules.

Conductance viewed as transmission

The domain of validity and the origin of different formulae relating conductance to transmissive behaviour is discussed. The large variety of possible measurement probes is emphasised. The quantised conductance of constrictions, studied in recent experiments, is treated. Theoretical discussions of that have stressed the supposedly unique role of G = (2e2/h)Tr(tt†) in this connection, regardless of the exact geometry or probe locations. This is shown to be incorrect, and a simple expression for the dependence of the 'quantised' conductance on the width of the wide region is given. We particularly emphasise the distinction between, on the one hand, experiments and discussions that are strictly limited to events at reservoirs and, on the other, those that have a concern with variations within the sample.

http://iopscience.iop.org/article/10.1088/0953-8984/1/43/011/pdf

R Landauer

Papers

Conductance determined by transmission: probes and quantised constriction resistance