Mesoscopic conductors

Feng. S. and P.A. Lees "Mesoscopic Conductors and Correlations in Laser Spackle Patients. . ScfVnrf. 633 (February 8, 199) 1. 

Summary. We discuss how threshold detectors can be used for a direct measurement of the full counting statistics (FCS) of current fluctuations and how to implement Josephson junctions in this respect. We propose a scheme to characterize the full counting statistics from the current dependence of the escape rate measured. We illustrate the scheme with explicit results for tunnel, diffusive and quasi-ballistic mesoscopic conductors. 

In this paper we address the feasibility of Josephson junction systems for measuring the FCS of a mesoscopic conductor. Our results are as follows. The Josephson junction is a realistic detector, all three factors mentioned are in play. Albeit one can measure FCS provided the width of the barrier 4>o 1. 

Fig. 1. A voltage biased mesoscopic conductor with conductance G provides the noise source for a threshold detector which is characterized by its threshold current Jth- lb is an additional current bias.

Fig. 2. Escape rates versus Th/T for a tunnel (t), diffusive (d) and ballistic (b) mesoscopic conductor. refers to forward/backward bias respectively. Dashed...

Landauer proposed in 1957 the first mesoscopic theoretical approach to charge transport [176]. Transport is treated as a scattering problem, ignoring initially all inelastic interactions. Phase coherence is assumed to be preserved within the entire conductor. Transport properties, such as the electrical conductance, are intimately related to the transmission probability for an electron to cross the system. Landauer considered the current as a consequence of the injection of electrons at one end of a sample, and the probability of the electrons reaching the other end. The total conductance is determined by the sum of all current-carrying eigenmodes and their transmission probability, which leads to the Landauer formula of a ID system ... 

Asymmetric conductors have isymmetric I — V curves. This phenomenon is known as the diode or ratchet effect and plays a major role in electronics. Recently much interest has been attracted by transport asymmetries in singlemolecule devices and other mesoscopic systems [1], The idea that asymmetric molecules can be used as rectifiers is rather old [2], however, it was implemented experimentally [3] only recently. Another experimental realization of a mesoscopic rectifier is an asymmetric electron waveguide constructed within the inversion layer of a semiconductor heterostructure [4]. The ratchet effect was observed in carbon nanotubes [5], and strongly asymmetric I — V curves were recently reported for the tunneling in the quantum Hall edge states [6]. These experimental advances have stimulated much theoretical activity [7, 8, 9, 10, 11] with the main focus on the simplest Fermi-liquid systems [12]. 

As the previous section showed, in a variety of examples severe enhancements of the ionic conductivity has been found and successfully attributed to space charge effects. Typical examples are silver halides or alkaline earth fluorides (see Section V.2.). How significantly these effects can be augmented by a particle size reduction, is demonstrated by the example of nano-crystalline CaF2.154 Epitaxial fluoride heterolayers prepared by molecular beam epitaxy not only show the thermodynamically demanded redistribution effect postulated above (see Section V.2.), they also highlight the mesoscopic situation in extremely thin films in which the electroneutral bulk has disappeared and an artificial ion conductor has been achieved (see Fig. 

Dye-sensitized systems are not suited to interpretation by conventional device physics methods on account of two features firstly, the mesoscopic phase separation of electron and hole conductors, which makes the porous material unable to sustain large electric fields and secondly, the separation, through the use of sensitizers, of optical absorption from charge transport in either material. Efforts to understand the photovoltaic action of the DSSC are leading to a reassessment of basic principles and the possibilities of novel photovoltaic designs. 

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