Jaynes-Cummings-Hubbard lattices provide unique properties for the study of correlated phases as they exhibit convenient state preparation and measurement, as well as "in situ" tuning of parameters. We show how to realize charge density and supersolid phases in Jaynes-Cummings-Hubbard lattices in the presence of long-range interactions. The long-range interactions are realized by the consideration of Rydberg states in coupled atom-cavity systems and the introduction of additional capacitive couplings in quantum-electrodynamics circuits. We demonstrate the emergence of supersolid and checkerboard solid phases, for calculations which take into account nearest neighbour couplings, through a mean-field decoupling.Comment: 9 pages with 6 figures, accepted for publication in Physical Review

Charge and spin transport in a junction involving two triplet superconductors and a ferromagnetic barrier are studied. We use Bogoliubov-de Gennes wavefunctions to construct the Green's function, from which we obtain the Josephson currents in terms of the Andreev reflection coefficients. We focus on the consequences of a finite barrier width for the occurrence of 0-π transitions and for the spin currents, and examine the appropriateness of the common δ-function approximation for the tunneling region.

We study the Josephson current in two types of lateral junctions with spin-orbit coupling and an exchange field. The first system (type 1 junction) consists of superconductors with heavy metal interlayers linked by a ferromagnetic bridge, such that the spin-orbit coupling is finite only at the superconductor/heavy metal interface. In the second type (type 2) of system we assume that the spin orbit coupling is finite in the bridge region. The length of both junctions is larger than the magnetic decay length such that the Josephson current is carried uniquely by the long-range triplet component of the condensate. The latter is generated by the spin-orbit coupling via two mechanisms, spin precession and inhomogeneous spin-relaxation. We show that the current can be controlled by rotating the magnetization of the bridge or by tuning the strength of the spin-orbit coupling in type 2 junctions., and also discuss how the ground-state of the junction can be tuned from a 0 to a π phase difference between the superconducting electrodes. In leading order in the spin-orbit coupling, the spin precession dominates the behavior of the triplet component and both junctions behave similarly. However, when spin relaxation effects are included junction of type 2 offers a wider parameter range in which 0-π transitions take place.

Although equilibrium spin currents (ESCs) may exist in materials with spin-orbit coupling, they are not transport currents and cannot lead to spin accumulation in the presence of time-reversal symmetry. It is for this reason that the detection of ESCs has remained elusive. Here we show that in a nanowire with spin-orbit coupling, breaking the time-reversal symmetry by a Zeeman field leads to a bulk equilibrium spin current which manifests itself in a sizable edge spin polarization, transverse to the Zeeman field. The net accumulated spin does not depend on specific properties of the wire ends, being fully determined by the bulk spin current. This bulk-boundary correspondence is a universal property that occurs in both the normal and superconducting states independently of the degree of disorder. The transverse edge spin polarization is strongly enhanced in the superconducting state when the Zeeman energy is of the order of the induced superconducting gap. This leads to a hitherto unknown transverse magnetic susceptibility that can be much larger than the longitudinal, and it drastically changes the paramagnetic response of the nanowire.

-The Andreev bound states and charge transport in a Josephson junction between two superconductors with intrinsic exchange fields are studied. We find that for a parallel configuration of the exchange fields in the superconductors the discrete spectrum consists of two pairs of spinsplit states. The Josephson current in this case is mainly carried by bound states. In contrast, for the antiparallel configuration we find that there is no spin-splitting of the bound states and that for phase differences smaller than certain critical value there are no bound states at all. Hence the supercurrent is only carried by states in the continuous part of the spectrum. Our predictions can be tested by performing a tunneling spectroscopy of a weak link between two spin-split superconductors.Introduction. -Superconductors with spin-split density of states have attracted particular interest since the pioneering works of Tedrow and Merservey, in which Zeeman splitting in superconductors was used to determine the spin-polarization of ferromagnetic metals [1,2]. Such spin-splitting can be achieved either by applying an external magnetic field or in thin superconducting films in contact with ferromagnetic insulators (FI) at zero field [3,4]. The spin-split density of states found in superconducting films originates from the exchange interaction between the conduction electrons of the superconductor and the large localised magnetic moments of the FI [5]. In order to obtain large spin-splittings, the use of FIs has the advantage of avoiding the application of high magnetic fields. The spectrum of a conventional superconductor in this case shows two BCS-like densities of states shifted by the energy 2h, where h is the effective exchange field induced in the superconductor film. Here we denote them as spin-split superconductors (SS).