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Nonequilibrium Effects in Mesoscopic Josephson Junctions

Doctoral thesis, 2001

In this thesis we present a unified scattering approach to current transport in mesoscopic Josephson junctions out of equilibrium. A nonequilibrium situation is created by either quasiparticle injection into the normal part of the junction, or by applying a dc-voltage between the two superconducting electrodes. The current is calculated from the scattering states, which are expressed in terms of the scattering matrix of the normal part of the junction and the Andreev reflection amplitudes at the normal conductor-superconductor (NS) interfaces.
The theory is first applied to a single mode ballistic Josephson junction with an additional normal lead connected to the normal part of the junction, and the effect on the Josephson current due to current injection from the normal lead is investigated. It is found that there are two main effects of the nonequilibrium. First, there is a nonequilibrium population of the current carrying Andreev levels which, dependent on junction length and injection voltage, can give a suppression, enhancement or even sign reversal of the Josephson current. Second, there is an anomalous nonequilibrium interference effect, which gives rise to a long range Josephson current, increasing with voltage eV up to the superconducting gap . The study is then extended to a two-dimensional ballistic junction and the sign reversal effect of the critical Josephson current is studied in detail.
Thereafter, the theory is applied to a three terminal a chaotic Josephson junction, where the normal part of the junction consists of a chaotic quantum dot. Using the statistical information of the scattering matrix of the dot, known from random matrix theory, the average nonequilibrium current and the sample-to-sample fluctuations of the current is studied. It is found that in junctions in the short dwell time regime, the average critical current is monotonically suppressed with increasing voltage, saturating at voltages at a value of order , where N is number of transverse modes in the contacts to the superconductor. At this voltage the critical current is entirely given from the anomalous interference current. The sample-to-sample fluctuations at this voltage is of the same order, which is a magnitude larger than the equilibrium current fluctuations.
Finally, a chaotic Josephson junction with a dc-voltage bias between the superconducting electrodes is studied, with the focus on the transition from a short to a long dwell time regime of the dot. It is found that a generic feature of the current voltage characteristics, besides the standard subharmonicic gap structures(SGS) at , is current anomalies at voltages of order of the Thouless energy away from the SGS with even subgap positions, n=2,4,6... These anomalies are suppressed by a magnetic field in the dot large enough to break time reversal symmetry (TRS). For broken TRS, it is found that the current takes on a universal value, independent on Thouless energy or magnetic field, exactly coinciding with the current found from the well known OTBK-model.