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Science

Flip-Flopping Fractional Flux Quanta

Thomas Ortlepp, Ariando Ariando, Olaf Mielke, C.J.M. Verwijs, Kok-Leei Foo, Horst Rogalla, Friedrich Uhlmann, Hans Hilgenkamp

Published Apr 21, 2006• 124 citations
Publisher

Abstract

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.

DOI
10.1126/science.1126041

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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.
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 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 report on the functionality of a Nb-based superconducting single flux quantum (SFQ) toggle flip-flop (TFF) circuit, comprising a complementary superconductor–ferromagnet–superconductor (SFS) Josephson π-junction. The SFS junction was used as a phase shifting element inserted in the storage loop of the TFF. The fabricated circuits demonstrated correct functionality with the operation parameter ranges of ± 20%. The application of SFS π-junctions makes the SFQ circuits very compact, may substantially improve their stability, and may also be suitable for integration with Josephson quantum circuits (qubits).
We have found that the size of some rapid single-flux quantum (RSFQ) logic cells based on conventional 0-type Josephson junctions can be significantly reduced by using a π-type junction as a phase shifter in passive (nonswitching) mode. In comparison with the recently suggested active (switching) π-junctions mode, the passive mode offers much greater operation margins for their critical current Icπ. This gives π-junctions a chance to be implemented in RSFQ designs in the near future. As an example, we have simulated the operation of a toggle flip flop with zero-geometrical inductance of the fluxon storage loop. Simulations show that the parametric inductance of the π-junction and its normal resistance Rn form a low-pass filter, which sets the low limit for π-junctions IcπRn product, but offers a wide range of variations of the other parameters. The possible reduction of RSFQ cell size by using π-junctions opens the way to scale superconducting logic circuits down to the submicron dimensions.
A methodology for designing single-flux-quantum (SFQ) flip-flops composed of both conventional (0-) and π -shifted Josephson junctions is investigated. We investigated the implementation of a storage loop, which can store flux quantum and is indispensable to express binary logic states in superconductor logic circuits. As all SFQ flip-flops have storage loops, the investigated design methodology can be applied to their design. We designed several SFQ flip-flops composed of 0- and π -shifted Josephson junctions using the investigated design methodology. The performances of the designed SFQ flip-flops were quantitatively evaluated by using an analog circuit simulator which we developed. We confirmed the correct operation of various SFQ flip-flops composed of 0- and π -shifted Josephson junctions with wide operating margins. Moreover, we observed that the investigated design methodology is suitable for SFQ flip-flops with complementary outputs because a storage loop composed of both 0- and π -shifted Josephson junctions has a symmetric structure and the complementary output function can be realized by using the storage loop. Our investigation indicates that the number of Josephson junctions and static power consumption of a non-destructive read-out flip-flop with complementary outputs (NDROC) can be reduced to less than half of those of the conventional NDROC, which has two storage loops composed of 0-Josephson junctions, to realize the complementary output function. The investigated design methodology is expected to be applied to not only SFQ circuits but also other superconducting logic circuits and novel reconfigurable logic devices using programmable 0- π Josephson junctions.