Josephson current through a long quantum wire

The dc Josephson current through a long SNS junction receives contributions from both Andreev bound states localized in the normal region as well as from scattering states incoming from the superconducting leads. We show that in the limit of a long junction, this current, at low temperatures, can be expressed entirely in terms of properties of the Andreev bound states at the Fermi energy: the normal and Andreev reflection amplitudes at the left-hand and at the right-hand S-N interface. This has important implications for treating interactions in such systems.Comment: 25 pages, 5 figure

Pairing of Cooper pairs in a Josephson junction network containing an impurity

We show how to induce pairing of Cooper pairs (and, thus, $4e$ superconductivity) as a result of local embedding of a quantum impurity in a Josephson network fabricable with conventional junctions. We find that a boundary double Sine-Gordon model provides an accurate description of the dc Josephson current patterns, as well as of the stable phases accessible to the network. We point out that tunneling of pairs of Cooper pairs is robust against quantum fluctuations, as a consequence of the time reversal invariance, arising when the central region of the network is pierced by a dimensionless magnetic flux $\phi = \pi$. We find that, for $\phi = \pi$, a stable attractive finite coupling fixed point emerges and point out its relevance for engineering a two level quantum system with enhanced coherence.Comment: 5 Pages, 5 Figures. Small modifications, ref.[11] added. To appear in EP

Linear Kondo conductance in a quantum dot

In a tunneling experiment across a quantum dot it is possible to change the coupling between the dot and the contacts at will, by properly tuning the trasparency of the barriers and the temperature. Gate voltages allow for changes of the relative position of the dot addition energies and the Fermi level of the leads. Here we discuss the two limiting cases: weak and strong coupling in the tunneling Hamiltonian. In the latter case Kondo resonant conductance can emerge at low temperature in a Coulomb blockade valley. We give a pedagogical approach to the single-channel Kondo physics at equilibrium and review the Nozieres scattering picture of the correlated fixed point. We emphasize the effect of an applied magnetic field and show how an orbital Kondo effect can take place in vertical quantum dots tuned both to an even and to an odd number of electrons at a level crossing. We extend the approach to the two-channel overscreened Kondo case and discuss recent proposals for detecting the non-Fermi liquid fixed point which could be reached at strong coupling.Comment: 31 pages, invited review articl

A general CFT model for antiferromagnetic spin-1/2 ladders with Mobius boundary conditions

We show how the low-energy properties of the 2-leg XXZ spin-1/2 ladders with general anisotropy parameter $\Delta$ on closed geometries can be accounted for in the framework of the m-reduction procedure developed in [1]. In the limit of quasi-decoupled chains, a conformal field theory (CFT) with central charge c=2 is derived and its ability to describe the model with different boundary conditions is shown. Special emphasis is given to the Mobius boundary conditions which generate a topological defect corresponding to non trivial single-spinon excitations. Then, in the case of the 2-leg XXX ladders we discuss in detail the role of various perturbations in determining the renormalization group flow starting from the ultraviolet (UV) critical point with c=2.Comment: 23 pages, 5 figures; J. Stat. Mech.: Theory Exp. (2008), in prin