Fluctuations in Mesoscopic Constrictions

Doctoral thesis, 1996

In normal and superconducting quantum point contacts there are several sources of fluctuations. Thermally activated impurities in the vicinity of the junction cause the current (or voltage) to change with a typical frequency of the order of one Hz up to a few kHz. Such temporal changes have been observed in normal quantum point contacts and are likely to appear in superconducting constrictions not yet realized. The first part of the thesis discusses a theoretical model for this type of fluctuations in both normal and superconducting micro-junctions. The effects of a single impurity as well as many impurities leading to 1/f-noise, are studied. Impurity noise is proposed as a probe of the interaction with the environment, but also as a test of transport in superconducting junctions. The transfer of charge through constrictions generates fluctuations of the current known as shot noise. The average current through voltage-biased superconducting quantum point contacts has recently been explained in terms of multiple Andreev reflections. In the latter part of the thesis, shot noise due to multiple Andreev reflections is calculated. From a general expression, the effects of normal reflection and temperature are deduced. Unusual effects are found: As the reflection is increased from zero, noise grows rapidly but also oscillates for voltages of the order of the superconducting pair potential .DELTA. . In utter contrast, the average current decreases with increasing reflection and is almost structureless for high transparencies. This suggests a non-existence of a general fluctuation-dissipation theorem for these contacts. Fluctuations within the energy gap (|E|<=.DELTA.) are proposed as a general explanation of these effects. Diagrammatic illustrations of contributing terms in shot noise are presented in the introduction.