Quantum of conductance

Here g, go, Tu, e, and h are respectively the conductance, the quantum of conductance equal to 77.48 microsiemens, the transmission through channel i, the electronic charge, and Planck s constant. The idea that conductance can be quantized is a remarkably new one compared with ohmic behavior - Fig. 6 shows experiments that directly demonstrate quantization of transport in atomic gold wires. 

For an ideal conductor, no scattering occurs, and the transmission is given by T = 1. The quantum of conductance Go is obtained, indicating a maximum conductance. In other words, a perfect single-channel conductor between two electrodes has a finite, non-zero resistance. The exact interpretation of this result was provided by Imry [177], who associated the finite resistance with resistance arising at the interface between leads and the electrodes. 

Fig. 14 The three-branches dianthra[a,c]naphtacene molecule circuit of symmetry formed by three anthracene fragments equivalently bonded to a central phenyl group. The molecule is adsorbed by the three branch ending phenyls onto the Au nano-pads. A semilogarithmic plot of the Tij(E) EHMO-NESQC electron transmission spectra (in valence energy range) per pair of branches. The presented frontier MOs show how the valence n electrons are delocalized on the molecule. At resonance, this provides a good electronic conductance through each pair of molecular branches, almost one quantum of conductance...

Here G0 = 2e2/h is the quantum of conductance and the factor 2 is due to spin degree of freedom. The current determined by Landauer formula is the elastic current. Indeed, we did not include any interactions leading to inelastic transport channels into the Hamiltonian. 

The transport properties of nanowires are of technological importance and have attracted significant attention in the recent years. Band structure gives simple solution to the analysis of the ballistic transport of periodic nanowires because the number of the bands crossing the Fermi surface is equal the number of quantum of conductance. However, the situation in nanocontacts is more complicated [112],... 

Nanotubes which have non-zero densities of states near the Fermi level should be electrical conductors [125,139]. However, in contrast to normal conductors, the conduction in SWNTs is predicted to be ballistic and may be quantized [144]. The quantization is in units of the quantum of conductance Go = 2e% = (12.9 kfl)". More specifically, in absence of scattering, the conductance of a nanotube G = NGq where N is the number of sub-bands which intercept the Fermi level, therefore G = 2Gq. Under these conditions, this predicts that the conductance of all SWNTs is 2Gq and hence, independent of length and diameter [144]. If a current is passed through a ballistic conductor there is no heating of the conductor itself, rather the Joule heat is dissipated in the reservoirs (i.e. the leads to the nanotube) [144]. 

The electron tunnelling probability between tip and sample is not small. In practice this occurs only when the electron transport is no longer dominated by tunnelling - either because a physical contact or nanojunction has been formed between the two, or because the tunnel barrier has collapsed completely (see above). The signature of this state of affairs is that the STM conductance becomes of the order of the quantum of conductance, e lh. 

One remarkable consequence appears to be that if the molecule lies in the middle of the barrier so that ri=rg, the conductance remains equal to the quantum of conductance (e /h) independent of tunneling distance. This is not the case in reality, because Equation 6.4 is only valid when the overlap integrals themselves are close to 1. r =Eg 1 corresponds to metallic bonding where electrons are indeed delocalized. Eor weaker coupling (normally the case in metal-molecule systems), we have to consider charging of the molecular state, with consequent change in its Coulomb energy. 

These quantum effects, though they do not generally affect significantly the magnitude of the resistivity, introduce new features in the low temperature transport effects [8]. So, in addition to the semiclassical ideal and residual resistivities discussed above, we must take into account the contributions due to quantum localisation and interaction effects. These localisation effects were found to confirm the 2D character of conduction in MWCNT. In the same way, experiments performed at the mesoscopic scale revealed quantum oscillations of the electrical conductance as a function of magnetic field, the so-called universal conductance fluctuations (Sec. 5.2). 

At low temperatures, in a sample of very small dimensions, it may happen that the phase-coherence length in Eq.(3) becomes larger than the dimensions of the sample. In a perfect crystal, the electrons will propagate ballistically from one end of the sample and we are in a ballistic regime where the laws of conductivity discussed above no more apply. The propagation of an electron is then directly related to the quantum probability of transmission across the global potential of the sample. 

As our quantum-chemical calculations show, similar transformation and delocalization of bonds takes place in the conductive forms of some other types of CPs (polyaniline, polypyrolle, etc.). Delocalization of chemical bonds after activation leads to appearance of an electronic conductivity in such types of conducting polymers and creates prerequisites for their application as electrode materials of electrochemical power sources. Such activation can be stimulated by intercalation of ions, applying the potential, and by use of some other low energetic factors. 

Charge transport through an array of semiconductor nanocrystals is strongly affected by the electronic structure of nanocrystal surfaces. It is possible to control the type of conductivity and doping level of quantum dot crystals by adsorbing/desorbing molecular species at the nanocrystal surface. As an... 

The AChR consists of five subunits surrounding an ion-conducting channel (Fig. 28.2). Activation of the binding sites on the two a-subunits results in a conformational change. This allows the simultaneous inflow of Na+ and Ca++ and outflow of K+, with a net inflow of positive charge. The response to a spontaneously secreted quantum of ACh (that is, activation of several thousand AChRs) is seen as a miniature EPC. With nerve stimulation, many quanta are released synchronously to produce a fuU-sized EPC, which is the sum-mated response of the 200 or so individual miniature EPCs. The EPC is a local graded current that in normal conditions triggers an action potential in the adjacent muscle membrane (Fig. 28.1). 

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