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We analyze the ground state properties of an array of quantum dots connected in series between superconducting electrodes. This system is represented by a finite Hubbard chain coupled at both ends to BCS superconductors. The ground state is obtained using the Lanczos algorithm within a low energy theory in which the bulk superconductors are replaced by effective local pairing potentials. We study the conditions for the inversion of the sign of the Josephson coupling ($pi$-junction behavior) as a function of the model parameters. Results are presented in the form of phase diagrams which provide a direct overall view of the general trends as the size of the system is increased, exhibiting a strong even-odd effect. The analysis of the spin-spin correlation functions and local charges give further insight into the nature of the ground state and how it is transformed by the presence of superconductivity in the leads. Finally we study the scaling of the Josephson current with the system size and relate these results with previous calculations of Josephson transport through a Luttinger liquid.
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The Josephson current through a 1D quantum wire with Rashba spin-orbit and electron-electron interactions is calculated. We show that the interplay of Rashba and Zeeman interactions gives rise to a supercurrent through the 1D conductor that is anomalous in the sense that it persists in the absence of any phase difference between the two superconducting leads to which it is attached. The electron dispersion asymmetry induced by the Rashba interaction in a Luttinger-liquid wire plays a significant role for poorly transmitting junctions. It is shown that for a weak or moderate electron-electron interaction the spectrum of plasmonic modes confined to the normal part of the junction becomes quasi-random in the presence of dispersion asymmetry.
We investigate the Josephson radiation emitted by a junction made of a quantum dot coupled to two conventional superconductors. Close to resonance, the particle-hole symmetric Andreev states that form in the junction are detached from the continuum above the superconducting gap in the leads, while a gap between them opens near the Fermi level. Under voltage bias, we formulate a stochastic model that accounts for non-adiabatic processes, which change the occupations of the Andreev states. This model allows calculating the current noise spectrum and determining the Fano factor. Analyzing the finite-frequency noise, we find that the model may exhibit either an integer or a fractional AC Josephson effect, depending on the bias voltage and the size of the gaps in the Andreev spectrum. Our results assess the limitations in using the fractional Josephson radiation as a probe of topology.
We study the Josephson current through a ferromagnetic trilayer, both in the diffusive and clean limits. For colinear (parallel or antiparallel) magnetizations in the layers, the Josephson current is small due to short range proximity effect in superconductor/ferromagnet structures. For non colinear magnetizations, we determine the conditions for the Josephson current to be dominated by another contribution originating from long range triplet proximity effect.
We review our recent studies on the Kondo effect in the tunneling phenomena through quantum dot systems. Numerical methods to calculate reliable tunneling conductance are developed. In the first place, a case in which electrons of odd number occupy the dot is studied, and experimental results are analyzed based on the calculated result. Tunneling anomaly in the even-number-electron occupation case, which is recently observed in experiment and is ascribed to the Kondo effect in the spin singlet-triplet cross over transition region, is also examined theoretically.
We discuss the behavior of a two-level system coupled to a quantum dot contacted by superconducting source/drain electrodes, representing a simple model for the conformational degree of freedom of a molecular dot or a break junction. The Josephson current is shown to induce conformational changes, including a complete reversal. For small bias voltage, periodic conformational motions induced by Landau-Zener transitions between Andreev states are predicted.
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