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Fractional flux quanta in high-Tc/low-Tc superconducting structures

C.J.M. Verwijs

Published Jun 25, 2009• 1 citation

Abstract

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.

DOI: 10.3990/1.9789090243160

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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.

The d-wave pairing symmetry in high-critical temperature superconductors makes it possible to realize superconducting rings with built-in pi phase shifts. Such rings have a twofold degenerate ground state that is characterized by the spontaneous generation of fractional magnetic flux quanta with either up or down polarity. We have incorporated pi phase-biased superconducting rings in a logic circuit, a flip-flop, in which the fractional flux polarity is controllably toggled by applying single flux quantum pulses at the input channel. The integration of p rings into conventional rapid single flux quantum logic as natural two-state devices should alleviate the need for bias current lines, improve device symmetry, and enhance the operation margins.

The latching of temporary data is essential in the rapid single flux quantum (RSFQ) electronics family. Its pulse-driven nature requires two or more stable states in almost all cells. Storage loops must be designed to have exactly two stable states for binary data representation. In conventional RSFQ such loops are constructed to have two stable states, e.g. by using asymmetric bias currents. This bistability naturally occurs when phase-shifting elements are included in the circuitry, such as π-Josephson junctions or a π-phase shift associated with an unconventional (d-wave) order parameter symmetry. Both approaches can be treated completely analogously, giving the same results. We have demonstrated for the first time the correct operation of a logic circuit, a toggle-flip-flop, using rings with an intrinsic π-phase shift (π-rings) based on hybrid high-Tcto low-TcJosephson junctions. Because of their natural bistability these π-rings improve the device symmetry, enhance operation margins and alleviate the need for bias current lines.

We fabricated Josephson junctions (JJs) between the d-wave superconductor (SC) YBa2Cu3O7-x (YBCO) and the s-wave SC Nb (ds-JJs) on graphoepitaxially buffered MgO substrates, studied ds-JJs at temperatures down to 30 mK and employed these JJs in π-loops. Current-voltage characteristics of ds-JJs oriented along the [100] axis of YBCO exhibited up to a factor of 200 higher critical current densities than ds-JJs oriented along the [110] axis of YBCO. The critical current

I_{c}

and the

I_{c}R_{n}

product of [100]-oriented 3 μm wide ds-JJs are ∼70 μA and ∼200 μV, respectively, at 4.2 K. Rectangular arrays of up to 40 000 π-loops based on such ds-JJs were investigated using a low temperature scanning superconducting quantum interference device (SQUID) microscope. We observed ordering of spontaneously generated half integer magnetic flux quanta in the π-loops correlated with minute spurious background magnetic fields, as well as with configurations and mutual coupling of the π-loops. We manipulated the magnetic states of the π-loops by the local application of magnetic fields using nearby planar coils. This paper paves the way for the use of π-loops in computations that are based on annealing processes.

The predominantly dx2−y2-pairing symmetry in most high-Tc superconductors provides the opportunity to fabricate Josephson junction circuits in which part of the junctions are biased by a phase difference of the superconducting order parameter of π. We present fabrication and measurements of an all high-Tc dc superconducting quantum interference device (dc SQUID) realized with thin-film technology, of which the Josephson junctions consist of one standard junction and one junction with a π-phase shift. The characteristics of the π-SQUID are compared with the properties of a standard high-Tc SQUID.

Abstract Half-flux-quantum (HFQ) circuits are based on 0–π superconducting quantum interference devices (SQUIDs) and is one of the energy-efficient superconductor digital circuits. The bit energy is determined by the critical current I cn of 0–π SQUID, which can be easily tuned with the loop inductance and junction critical current. In this work, an alternative π–π–π SQUID is adopted to demonstrate HFQ circuits to simplify the fabrication process and enhance circuit energy efficiency. The properties of superconductor/ferromagnet/insulator/superconductor Josephson junctions (π-JJs) are measured with temperature dependence from 4.2 K down to 10 mK. HFQ toggle flip-flops (TFFs) are successfully demonstrated at frequencies of up to 6.7 GHz and 44.5 GHz at temperatures of 4.2 K and 10 mK, respectively. Comparing the HFQ TFF with its rapid single-flux quantum counterpart under the same fabrication process, it is anticipated that the HFQ TFF will exhibit approximately 70% reduction in both static and dynamic energy dissipation. This research establishes the foundation for developing cryogenic interface control and readout circuits for large-scale quantum computing in the future.

Superconducting quantum interference devices (SQUIDs) have been realized with a built-in π∕2 phase shift of the superconducting wave function. Its design is inspired by the phase-shifter concept, first proposed by Ioffe et al. [Nature 398, 679 (1999)] as the key element in a solid-state qubit configuration. It exploits the dx2−y2 order parameter symmetry in the high-Tc cuprates in multilayer structures based on YBa2Cu3O7-Nb ramp-type Josephson contacts. By reversing the sign of the persistent circulating current in the phase-shifting element, the π∕2 SQUID can be controllably switched between two energetically degenerate ground states, with complementary magnetic flux dependencies.