Phase-slip lines can be viewed as dynamically created Josephson junctions in a homogeneous superconducting film. In contrast to phase-slip centers, phase-slip lines occur in wide superconducting strips, where the order parameter may vary in two dimensions. We investigated phase-slip lines in two different materials using several methods. We observed Shapiro steps under microwave radiation, which shows that the frequency of the order parameter oscillation is equal to Josephson frequency. A periodic oscillation of a critical current versus the applied magnetic field was found in strips with a hole in the middle. The latter effect provides a clear evidence of macroscopic quantum interference across a phase-slip line. We have used low temperature scanning laser microscopy to visualize the phase-slip lines and to distinguish them from possible local inhomogeneities in the films.

We compare the results of ground state and spectroscopic measurements carried out on superconducting flux qubits which are effective two-level quantum systems. For a single qubit and for two coupled qubits we show excellent agreement between the parameters of the pseudospin Hamiltonian found using both methods. We argue that by making use of the ground state measurements the Hamiltonian of N coupled flux qubits can be reconstructed as well at temperatures smaller than the energy level separation. Such a reconstruction of a many-qubit Hamiltonian can be useful for future quantum information processing devices.

We have measured the current-phase relationship I(ϕ) of symmetric 45 • YBa2Cu3O7−x grain boundary Josephson junctions. Substantial deviations of the Josephson current from conventional tunnel-junction behavior have been observed: (i) The critical current exhibits, as a function of temperature T , a local minimum at a temperature T * . (ii) At T ≈ T * , the first harmonic of I(ϕ) changes sign. (iii) For T < T * , the second harmonic of I(ϕ) is comparable to the first harmonic, and (iv) the ground state of the junction becomes degenerate. The results are in good agreement with a microscopic model of Josephson junctions between d-wave superconductors.The most important phenomenological difference between the high-T c cuprates and conventional superconductors regards the orbital symmetry of the superconducting order parameter. In the cuprates the pair potential changes sign depending on the direction in momentum space according to 1,2 ∆(ϑ) = ∆ 0 cos 2(ϑ − θ), where ϑ is the angle between the wave vector and the (laboratory) x-axis, while θ is the angle between the Cu-Cu bond direction of the superconductor and the x-axis. This unconventional d-wave symmetry was predicted 3 and experimentally confirmed 1,2 to be directly measurable in the Josephson effect between a high-T c and a conventional superconductor. Another consequence of the dwave symmetry is that mid-gap states (MGS) with energy ε = 0 should form on the free surface of a d-wave superconductor if ∆(ϑ) has opposite signs on incident and reflected electronic trajectories. 4 The MGS density must be maximal for (110)-like surfaces and this prediction has in fact been confirmed by STM microscopy on YBCO single crystals 5 which revealed the MGS contribution to the YBCO tunneling density of states. The presence of the MGS is expected to influence in a spectacular way also the Josephson effect in junctions between d-wave superconductors with different crystallographic orientations. Yet no clear manifestation of the MGS in the Josephson effect in such junctions has been observed so far, which is a challenge for the concept of d-wave superconductivity in the cuprates.Moreover, due to possible applications in quantum computing, 6,7 there is substantial interest in Josephson junctions and circuits with a doubly degenerate ground state. Such a state was predicted in an asymmetric 45 • junction (θ 1 = 0 • and θ 2 = 45 • , the angles θ 1,2 are defined in Fig. 1), since odd harmonics of the Josephson current I(ϕ) = n I n sin nϕ are suppressed by symmetry. 8,9The current-phase relation observed in Ref. 10 indeed showed a substantial contribution of the second harmonic I 2 . However, there is a finite supercurrent flowing along the interface in the ground state of asymmetric 45 • junctions. 9 Therefore they do not lead to completely quiet qubits in the sense of Ref. 6. Motivated by the search for both, the MGS in high-T c Josephson junctions and a quiet qubit, we have studied symmetric 45 • junctions (i.e. junctions with θ 1 = −θ 2 = 22.5 • ). In this paper we report the fir...

A boundary between two d-wave superconductors or an s-wave and a d -wave superconductor generally breaks time-reversal symmetry and can generate spontaneous currents due to proximity effect. On the other hand, surfaces and interfaces in d-wave superconductors can produce localized current-carrying states by supporting the T -breaking combination of dominant and subdominant order parameters. We investigate spontaneous currents in the presence of both mechanisms and show that at low temperature, counter-intuitively, the subdominant coupling decreases the amplitude of the spontaneous current due to proximity effect. Superscreening of spontaneous currents is demonstrated to be present in any d-d (but not s-d) junction and surface with d + id ′ order parameter symmetry. We show that this supercreening is the result of contributions from the local magnetic moment of the condensate to the spontaneous current.(May 29, 2018)The time-reversal symmetry (T ) breaking on surfaces and interfaces of superconductors with d-wave orbital pairing has been intensively investigated in the last years both in theory and experiment [1][2][3][4][5][6][7][8]. Several mechanisms of T -breaking have been proposed, which fall in two categories: appearance of subdominant order parameter and proximity effect [2,3].In the first case the surface or interface suppresses the dominant order parameter (d x 2 −y 2 in YBCO [4]). If the pairing interaction in other channels is nonzero, the subdominant order parameter will be formed below the corresponding, smaller critical temperature T c2 [9]. The combination of the two order parameters with complex coefficients breaks the T -symmetry [1] and leads to spontaneous surface currents and magnetic fluxes. Usually d x 2 −y 2 ± is or d x 2 −y 2 ± id xy combinations are predicted. Recent observations of zero bias peak splitting in surface tunneling experiments [5] and spontaneous fractional flux (0.1-0.2 Φ 0 ) near the "green phase" inclusions in YBCO films [6] agree with this picture.The other possibility arises in a junction between two d-wave superconductors with different orientations of the order parameter [7]. In this case the two order parameters necessary to form a T -breaking state, d 1,2 , are supplied by the bulk superconductors. The equilibrium phase difference across the boundary, φ 0 , is generally neither 0 nor π, and therefore the states with d 1 +e ±iφ0 d 2 orderings are degenerate and may support spontaneous currents. The same mechanism applies in case of a boundary between an s-and a d-wave superconductor [8].In order to investigate the interplay of both mechanisms, in this letter we consider d-d and s-d interfaces as well as (110)-surface of a d-wave superconductor. We will see that generally the spontaneous currents due to proximity effect are suppressed by the existence of subdominant order parameter. There is also an important distinction between the d-d and s-d cases: In the former case the superconductor may have local orbital and magnetic moments, contributing to the non-dissipative...

The work describes the capabilities of Laser Scanning Microscopy (LSM) as a spatiallyresolved method of testing high-T c materials and devices. The earlier results obtained by the authors are briefly reviewed. Some novel applications of the LSM are illustrated, including imaging the HTS responses in rf mode, probing the superconducting properties of HTS single crystals, development of two-beam laser scanning microscopy. The existence of the phase slip lines mechanism of resistivity in HTS materials is proven by LSM imaging.

We investigate the properties of spontaneous currents generated at surfaces and interfaces of d-wave superconductors using the self-consistent quasiclassical Eilenberger equations. The influence of the roughness and reflectivity of the boundaries on the spontaneous current are studied. We show that these have very different effects at the surfaces compared to the interfaces, which reflects the different nature of the time reversal symmetry breaking states in these two systems. We find a signature of the "anomalous proximity effect" at rough d-wave interfaces. We also show that the existence of a subdominant order parameter, which is necessary for time reversal symmetry breaking at the surface, suppresses the spontaneous current generation due to proximity effect at the interface between two superconductors. We associate orbital moments to the spontaneous currents to explain the "superscreening" effect, which seems to be present at all ideal d-wave surfaces and interfaces, where dxy is the favorite subdominant symmetry.

We investigated both theoretically and experimentally dynamic features of a phase-biased charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop. The effective inductance of the qubit was probed by a high-quality tank circuit. In the presence of a microwave power, with a frequency of the order of the qubit energy level separation, an alteration of the qubit inductance was observed. We demonstrate that this effect is caused by the redistribution of the qubit level population. The excitation of the qubit by one-, two-, and three-photon processes was detected. Quantitative agreement between theory and experimental data was found.

The d.c. Josephson effect in superconducting microbridges has been studied in terms of the microscopic theory of superconductivity. Current-phase relation, I (ϕ), and a critical current value, Ic(T), have been obtained and shown to be different from those quantities corresponding to the tunnel junction. These differences are most pronounced at low temperatures and for the pure constrictions : l≫a, l : being the electron mean free path and a : the radius of the orifice connecting two superconductors. In the latter case [MATH