When the conventional superconductor niobium and the cuprate superconductor YBa2Cu3O7-δ (YBCO) are connected in a ring-shaped geometry, the ground state is characterized by a spontaneously generated current corresponding to a half-integer magnetic flux quantum in the large inductance limit. The spontaneously generated currents result from a π-phase shift originating from the difference in order parameter symmetry for niobium (s-wave) and YBCO (dx2-y2-wave). The fractional magnetic flux quanta in high-Tc/low-Tc superconducting structures have been used for an angle-resolved phase sensitive study to the order parameter symmetry in YBCO, which was found to contain an s-wave admixture of at least 9%. Moreover, the experiments set an upper limit of a few percent on any complex admixture. The fractional flux quanta have also been used for the realization of a novel superconducting logic circuit element: a toggle flip-flop with integrated π-rings. The dx2-y2-wave-induced π-phase shifts alleviate the need for bias current lines and improve design-, fabrication- and operation margins. The π-ring-based toggle flip-flop has been integrated in a test circuit and its correct operation was demonstrated. Besides in π-rings, the fractional magnetic flux quanta have also been studied in a so-called corner geometry. The first on-chip manipulation and read-out of half-integer flux quanta in a 0-π-0 junction is presented. This is an important step forward if corner junctions are to be integrated in superconducting electronics.
Abstract We propose the Josephson junctions linked by a normal metal between a d + id superconductor and another d + id superconductor, a d-wave superconductor, or a s-wave superconductor for identifying the chiral d + id superconductivity. The time-reversal breaking in the chiral d-wave superconducting state is shown to result in a Josephson φ0-junction state where the current-phase relation is shifted by a phase φ0 from the sinusoidal relation, other than 0 and π. The ground-state phase difference φ0 and the critical current can be used to definitely confirm and read the information about the d + id superconductivity. A smooth evolution from conventional 0-π transitions to tunable φ0-states can be observed by changing the relative magnitude of two types of d-wave components in the d + id pairing. On the other hand, the Josephson junction involving the d + id superconductor is also the simplest model to realize a φ0- junction, which is useful in superconducting electronics and superconducting quantum computation.
Recently, a new theory of superconductivity has been put forward that attributes the origin of superconductivity to the appearance of a non-trivial Berry connection from many-electron wave functions. This theory reproduces the major results of the BCS theory with conserving the particle number, and predicts the single-electron supercurrent tunneling across the Josephson junction with keeping the correct Josephson relation. We re-examine the quantization of superconducting qubit circuits by taking into account the above development, and show that the dynamical variables used in the standard theory, the flux nodes relating to the voltage, should be replaced by those relating to the electromagnetic vector potential. The fact that the Josephson junction tunneling allows the single-electron supercurrent tunneling is the reason for the existence of excited single electrons in superconducting qubits with Josephson junctions. We predict that it will be avoided by weakening the coupling between two superconductors in the Josephson junction.
We study quantum phase-slip (QPS) processes in a superconducting ring containing
N Josephson junctions and threaded by an external static magnetic flux ${\ensuremath{\Phi}}_{B}$. In such a system, a QPS consists of a quantum tunneling event connecting two distinct classical states of the phases with different persistent currents [Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson coupling energy
EJ of the junctions is larger than the charging energy
EC=e2/2C, where
C is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio
EJ/EC. At given magnetic flux, each QPS can be described as the tunneling of the phase difference of a single junction of almost $2\ensuremath{\pi}$, accompanied by a small harmonic displacement of the phase difference of the other $N\ensuremath{-}1$ junctions. As a consequence, the total QPS amplitude ${\ensuremath{\nu}}_{\mathrm{ring}}$ is a global property of the ring. Here, we study the dependence of ${\ensuremath{\nu}}_{\mathrm{ring}}$ on the ring size
N, taking into account the effect of a finite capacitance
C0 to ground, which leads to the appearance of low-frequency dispersive modes. Josephson and charging effects compete and lead to a nonmonotonic dependence of the ring's critical current on
N. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy
E0=e2/2C0 and the Josephson coupling energy
EJ.
In some textbooks on quantum mechanics, the description of flux quantization in a superconductor ring based on the Aharonov-Bohm effect may lead some readers to a (wrong) conclusion that flux quantization occurs as well for a long solenoid with the same quantization condition in which the charge of cooper pair
2e is replaced by the charge of one electron
e. It is shown how this confusion arises and how can one avoid it.
We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.