Periodic alternating 0,π0,\pi-junction structures as realization of ϕ\phi-Josephson junctions

We consider the properties of a periodic structure consisting of small alternating 0- and pi- Josephson junctions. We show that depending on the relation between the lengths of the individual junctions, this system can be either in the homogeneous or in the phase-modulated state. The modulated phase appears via a second order phase transition when the mismatch between the lengths of the individual junctions exceeds the critical value. The screening length diverges at the transition point. In the modulated state, the equilibrium phase difference in the structure can take any value from -pi to pi (phi-junction). The current-phase relation in this structure has very unusual shape with two maxima. As a consequence, the field dependence of the critical current in a small structure is very different from the standard Fraunhofer dependence. The Josephson vortex in a long structure carries partial magnetic flux, which is determined by the equilibrium phase.Comment: 4 pages, 3 figues, submitted to Phys. Rev.

Ground state and bias current induced rearrangement of semifluxons in 0-pi long Josephson junctions

We investigate numerically a long Josephson junction with several phase pi-discontinuity points. Such junctions are usually fabricated as a ramp between an anisotropic cuprate superconductor like YBCO and an isotropic metal superconductor like Nb. From the top, they look like zigzags with pi-jumps of the Josephson phase at the corners. These pi-jumps, at certain conditions, lead to the formation of half-integer flux quanta, which we call semifluxons (SF), pinned at the corners. We show (a) that the spontaneous formation of SFs depends on the junction length, (b) that the ground state without SFs can be converted to a state with SFs by applying a bias current, (c) that the SF configuration can be rearranged by the bias current. All these effects can be observed using a SQUID microscope.Comment: ~8 pages, 6 figures, submitted to PR

Paramagnetic effect in YBaCuO grain boundary junctions

A detailed investigation of the magnetic response of YBaCuO grain boundary Josephson junctions has been carried out using both radio-frequency measurements and Scanning SQUID Microscopy. In a nominally zero-field-cooled regime we observed a paramagnetic response at low external fields for 45 degree asymmetric grain boundaries. We argue that the observed phenomenology results from the d-wave order parameter symmetry and depends on Andreev bound states.Comment: To be published in Phys. Rev.

Induced paramagnetic states by localized π\pi -loops in grain boundaries

Recent experiments on high-temperature superconductors show paramagnetic behavior localized at grain boundaries (GB). This paramagnetism can be attributed to the presence unconventional d-wave induced $\pi$-junctions. By modeling the GB as an array of $\pi$ and conventional Josephson junction we determine the conditions of the occurrence of the paramagnetic behavior.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Fluxoid dynamics in superconducting thin film rings

We have measured the dynamics of individual magnetic fluxoids entering and leaving photolithographically patterned thin film rings of the underdoped high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, using a variable sample temperature scanning SQUID microscope. These results can be qualitatively described using a model in which the fluxoid number changes by thermally activated nucleation of a Pearl vortex in, and transport of the Pearl vortex across, the ring wall.Comment: 9 pages, 10 figures, fixed typo

Dynamical effects of an unconventional current-phase relation in YBCO dc-SQUIDs

The predominant d-wave pairing symmetry in high temperature superconductors allows for a variety of current-phase relations in Josephson junctions, which is to a certain degree fabrication controlled. In this letter we report on direct experimental observations of the effects of a non-sinusoidal current-phase dependence in YBCO dc-SQUIDs, which agree with the theoretical description of the system.Comment: 4 pages, 4 ps figures, to apprear in Phys. Rev. Let

Quantum phase transitions from topology in momentum space

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy corner does not depend on the complicated details of the system and is relatively simple. It is determined by the nodes in the fermionic spectrum, which are protected by topology in momentum space (in some cases, in combination with the vacuum symmetry). Close to the nodes the behavior of the system becomes universal; and the universality classes are determined by the toplogical invariants in momentum space. When one changes the parameters of the system, the transitions are expected to occur between the vacua with the same symmetry but which belong to different universality classes. Different types of quantum phase transitions governed by topology in momentum space are discussed in this Chapter. They involve Fermi surfaces, Fermi points, Fermi lines, and also the topological transitions between the fully gapped states. The consideration based on the momentum space topology of the Green's function is general and is applicable to the vacua of relativistic quantum fields. This is illustrated by the possible quantum phase transition governed by topology of nodes in the spectrum of elementary particles of Standard Model.Comment: 45 pages, 17 figures, 83 references, Chapter for the book "Quantum Simulations via Analogues: From Phase Transitions to Black Holes", to appear in Springer lecture notes in physics (LNP

Orthogonality constrained inverse regression to improve model selectivity and analyte predictions from vibrational spectroscopic measurements

In analytical chemistry spectroscopy is attractive for high-throughput quantification, which often relies on inverse regression, like partial least squares regression. Due to a multivariate nature of spectroscopic measurements an analyte can be quantified in presence of interferences. However, if the model is not fully selective against interferences, analyte predictions may be biased. The degree of model selectivity against an interferent is defined by the inner relation between the regression vector and the pure interfering signal. If the regression vector is orthogonal to the signal, this inner relation equals zero and the model is fully selective. The degree of model selectivity largely depends on calibration data quality. Strong correlations may deteriorate calibration data resulting in poorly selective models. We show this using a fructose-maltose model system. Furthermore, we modify the NIPALS algorithm to improve model selectivity when calibration data are deteriorated. This modification is done by incorporating a projection matrix into the algorithm, which constrains regression vector estimation to the null-space of known interfering signals. This way known interfering signals are handled, while unknown signals are accounted for by latent variables. We test the modified algorithm and compare it to the conventional NIPALS algorithm using both simulated and industrial process data. The industrial process data consist of mid-infrared measurements obtained on mixtures of beta-lactoglobulin (analyte of interest), and alpha-lactalbumin and caseinoglycomacropeptide (interfering species). The root mean squared error of beta-lactoglobulin (% w/w) predictions of a test set was 0.92 and 0.33 when applying the conventional and the modified NIPALS algorithm, respectively. Our modification of the algorithm returns simpler models with improved selectivity and analyte predictions. This paper shows how known interfering signals may be utilized in a direct fashion, while benefitting from a latent variable approach. The modified algorithm can be viewed as a fusion between ordinary least squares regression and partial least squares regression and may be very useful when knowledge of some (but not all) interfering species is available