Landauer resistance

Tunneling and the Landauer Resistance Quantum. Across nanoscopic gaps (vacuum, or atoms or molecules for distances of the order of 5 nm or less), Ohm s law will no longer apply The TV curve will be nonlinear, the conductance could be "ballistic" (i.e., free from scattering events), and the main mechanism is quantum-mechanical tunneling. Landauer21 proved in 1957 that (in later terminology) a "metal-molecule-metal" or a "metal-nanowire-metal" sandwich allows [10] a maximum current T. 

The main results are that a reduction in particle size at one position of the array increases the potential at this point which may lead, at least, to localization, i. e. the single excess electron in the array might be trapped. At a packing defect, which affects the inter-particle capacitance at one point and acts like an inhomogenity, the soliton will interact with its mirror-image soliton (or anti-soliton) and will therefore be attracted. Concerning the practical use of this method, it was emphasized that the total reflection amplitude obtained from these calculations is directly related to the Landauer resistance,and reflects the electrical characteristics of such multijunction arrays. 

Landauer, R., 1952. The electrical resistance of binary metallic mixtures, J. Appl. Phys., 23, 779-784. 

ELECTRICAL RESISTANCE, HALL EFFECT, DRUDE MODEL, TUNNELING, AND THE LANDAUER FORMULA... 

Landauer, R. (1970) Electrical resistance of disordered one-dimensional lattices. Philos. Mag., 21, 863-867. 

Landauer R (1989) Conductance determined by transmission probes and quantised constriction resistance. J Phys Condens Matter 1 8099... 

Rolf Landauer proved that the minimum resistance of any single-channel wire (composed of atoms or molecules or polymers), measured between any two macroscopic electrodes, is the quantum of resistance R = (h/2e ) = 12.91 kQ, where h is Planck s constant, and e is the electronic charge. In Milestone Two, this Landauer quantum of resistance was measured by Walt de Heer and coworkers at room temperature between a multiple-walled carbon nanotube (MWCNT), glued to a conducting AFM tip, and a pool of liquid... 

According to Samanta et ol. [62], who used a GF-based method to calculate the transmission function of electrons across the dithiol ligand, the resistance R per molecule was determined by the Landauer formula, R = hl2e )IT(Eg), where T( g) is the transmission function, T exp[2(m g) /H]. For the dithiol molecule, the barrier height was estimated to be g 2.8eV, and the resulting resistance calculated as R 30GQ. 

A major improvement in the STM procedure produced SPBJ histograms of STM currents (Figure 4) measured between an Au(lll) surface and an Au nanotip immersed in a 0.1-M NaC104 solution " when the gap is closed by an Au filament (Figure 4a,b) then maxima in the conductance can be seen near zero bias (V = 0.013 V), in units of the Landauer conductance quantum Gl = 2e /h (4) for one filament (Gl), two filaments in parallel (2 Gl), or three filaments in parallel (3 Gl). When the An filament is absent, but the solution is made 1 mM in 4,4-bipyridine (10), where bonds can be made between the Au electrodes and the two N atoms, then conductance maxima are seen at 0.01 Gl, 0.02 Gl, and 0.03 Gl this corresponds to a molecular resistance of 1.3 0.1MS2 per 4,4 -bipyridine molecule. As the bias is increased. 

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