Evidence for Triplet Superconductivity in a Superconductor-Ferromagnet Spin Valve

We have studied the dependence of the superconducting (SC) transition temperature on the mutual orientation of magnetizations of Fe1 and Fe2 layers in the spin valve system CoO_x/Fe1/Cu/Fe2/Pb. We find that this dependence is nonmonotonic when passing from the parallel to the antiparallel case and reveals a distinct minimum near the orthogonal configuration. The analysis of the data in the framework of the SC triplet spin valve theory gives direct evidence for the long-range triplet superconductivity arising due to noncollinearity of the two magnetizations.Comment: 5 pages (including 4 EPS figures). Version 2: final version as published in PR

Density of states in d-wave superconductors of finite size

We consider the effect of the finite size in the ab-plane on the surface density of states (DoS) in clean d-wave superconductors. In the bulk, the DoS is gapless along the nodal directions, while the presence of a surface leads to formation of another type of the low-energy states, the midgap states with zero energy. We demonstrate that finiteness of the superconductor in one of dimensions provides the energy gap for all directions of quasiparticle motion except for \theta=45 degrees (\theta is the angle between the trajectory and the surface normal); then the angle-averaged DoS behaves linearly at small energies. This result is valid unless the crystal is 0- or 45-oriented (\alpha \ne 0 or 45 degrees, where \alpha is the angle between the a-axis and the surface normal). In the special case of \alpha=0, the spectrum is gapped for all trajectories \theta; the angle-averaged DoS is also gapped. In the special case of \alpha=45, the spectrum is gapless for all trajectories \theta; the angle-averaged DoS is then large at low energies. In all the cases, the angle-resolved DoS consists of energy bands that are formed similarly to the Kronig-Penney model. The analytical results are confirmed by a self-consistent numerical calculation.Comment: 9 pages (including 5 EPS figures), REVTeX

Decoherence due to nodal quasiparticles in d-wave qubits

We study the Josephson junction between two d-wave superconductors, which is discussed as an implementation of a qubit. We propose an approach that allows to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor.Comment: 5 pages, 3 EPS figures; the style file jetpl.cls is included. Version 2: minor correction

Peculiarities of the density of states in SN junctions

We study the density of states (DoS) $\nu(E)$ in a normal-metallic (N) film contacted by a bulk superconductor (S). We assume that the system is diffusive and the SN interface is transparent. In the limit of thin N layer (compared to the coherence length), we analytically find three different types of the DoS peculiarity at energy equal to the bulk superconducting order parameter $\Delta_0$. (i) In the absence of the inverse proximity effect, the peculiarity has the check-mark form with $\nu(\Delta_0)=0$ as long as the thickness of the N layer is smaller than a critical value. (ii) When the inverse proximity effect comes into play, the check-mark is immediately elevated so that $\nu(\Delta_0)>0$. (iii) Upon further increasing of the inverse proximity effect, $\nu(E)$ gradually evolves to the vertical peculiarity (with an infinite-derivative inflection point at $E=\Delta_0$). This crossover is controlled by a materials-matching parameter which depends on the relative degree of disorder in the S and N materials.Comment: 20 pages, 8 figures. Version 2: updated Introduction and Conclusions, added Discussion section (on experimental relevance) and references. Final version as published in Annals of Physic

Asymmetric higher-harmonic SQUID as a Josephson diode

We theoretically investigate asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics. Our main focus is on the "minimal model" with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. The current-voltage characteristic (CVC) turns out to be asymmetric, $I(-V) \neq -I(V)$. The asymmetry is due to the presence of the second harmonic and depends on the magnetic flux through the interferometer loop, vanishing only at special values of the flux such as integer or half-integer in the units of the flux quantum. The system thus demonstrates the flux-tunable Josephson diode effect (JDE), the simplest manifestations of which is the direction dependence of the critical current. We analyze asymmetry of the overall $I(V)$ shape both in the absence and in the presence of external ac irradiation. In the voltage-source case of external signal, the CVC demonstrates the Shapiro spikes. The integer spikes are asymmetric (manifestation of the JDE) while the half-integer spikes remain symmetric. In the current-source case, the CVC demonstrates the Shapiro steps. The JDE manifests itself in asymmetry of the overall CVC shape, including integer and half-integer steps.Comment: 18 pages, 5 figures. Version 2: extended introduction, added references. Final version as published in PR