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CRC Press eBooks

Superconducting Quantum Interference Devices

J. C. Gallop

Published Oct 19, 2017• 5 citations
Publisher

Abstract

In Chapter 2 we made use of a hypothetical arrangement of a strongly coupled superconducting ring, interrupted by a region of weak superconductivity, to derive the essential features of the Josephson effects. In practice this same arrangement is actually employed as the basis of one of the most useful superconducting devices developed so far, the single-junction, or rf, squid . (As mentioned in the Introduction, squid is an acronym for Superconducting QUantum Interference Device.) Here the essential physics behind the operation of these important devices will be described, and in the following section the practical realisation of an rf squid with its associated readout electronics will be explained. Chapter 4 will treat in a similar way dc squid s, which are related devices possessing two weak links in a single ring, whose mode of operation is rather different.

DOI
10.1201/9780203738887-3

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Variable superconducting quantum-interference device: Theory

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A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents ${I}_{1}$ and ${I}_{2}$, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current ${I}_{2}$ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current ${I}_{1m}$(\ensuremath{\varphi}). For values of ${I}_{2}$>${I}_{c}$ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.

Physical review. B, Condensed matter•Jul 1, 1987•5 citations
In Chapter 2 we made use of a hypothetical arrangement of a strongly coupled superconducting ring, interrupted by a region of weak superconductivity, to derive the essential features of the Josephson effects. In practice this same arrangement is actually employed as the basis of one of the most useful superconducting devices developed so far, the single-junction, or rf, squid . (As mentioned in the Introduction, squid is an acronym for Superconducting QUantum Interference Device.) Here the essential physics behind the operation of these important devices will be described, and in the following section the practical realisation of an rf squid with its associated readout electronics will be explained. Chapter 4 will treat in a similar way dc squid s, which are related devices possessing two weak links in a single ring, whose mode of operation is rather different.
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.
We have already seen, in Chapter 2 , that the complex response of a Josephson junction to applied electromagnetic radiation forms a basis for both broad-band and heterodyne detection modes, ranging from low frequencies to the far-infrared. Greater detail of actual working devices of this type will be given in this chapter. The second topic dealt with is digital applications of squid s. This is already a significant, and may in the future become a dominant, use of low-power superconducting technology. At first sight the contents of this chapter may seem to divide into two rather disconnected areas. However, logic devices have two important characteristics in common with radiation detectors: first, both involve very high-frequency operation, since slow digital devices are of little or no practical interest. Second, both applications demand the use of well characterised and reproducible small-area junctions with similar parameters. In what follows, more details of junction fabrication methods will be given than have been discussed earlier in the book. This reflects the fact that well defined junction properties are of the utmost importance in achieving high performance in these areas. It seems paradoxical that squid s, for all their unparalleled sensitivity, will operate very satisfactorily with far from ideal Josephson junctions. This is mainly because squid s have only been used in rather low-frequency applications, for which the low resistive and reactive impedances associated with poor-quality junctions do not limit performance.
Nanoscale superconducting quantum interference devices (nano-SQUIDS) where the weak links are made from nanobridges, i.e., nanobridge SQUIDs (NBSs), are one of the most sensitive magnetometers for nanoscale magnetometry. Because of very strong nonlinearity in the nanobridge-electrode joints, the applied magnetic flux (${\mathrm{\ensuremath{\Phi}}}_{a}$)--critical current (Ic{I}_{c}Ic​) characteristics of NBSs differ very significantly from conventional tunnel-junction SQUIDs, especially when the nanobridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated as the conventional tunnel-junction SQUIDs, which are based on the dc Josephson effect. Here, I present a model demonstrating that for long nanobridges and/or large screening parameters the ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$ of a NBS can be explained by merely considering the fluxoid quantization in the NBS loop and the energy of the NBS; it is not necessary to take the Josephson effect into consideration. I also demonstrate that using the model, one can derive useful expressions such as the modulation depth and transfer function. I discuss the role of the kinetic inductance fraction ($\ensuremath{\kappa}$) in determining ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$. I compare the predictions of the present model with the experimental data already published by several groups.
Operation principle of AND/OR logic has been realized in a coupled high-T c Superconducting QUantum Interference Device (SQUID). The device consists of rf- and dc-SQUID's. The logic operation is based on the nonlinear characteristics of the internal and external magnetic flux in the rf-SQUID. Results of the logic operation can be read out by the dc-SQUID. The device is made of NdBa2Cu3O7-δ superconducting thin film with superconducting weak links fabricated using a narrow-focused Ga-ion beam technology.
The development of superconducting electronics requires careful characterization of the components that makeup electronic circuits. Superconducting weak links are the building blocks of most superconducting electronic components and are characterized by highly nonlinear current-to-phase relations (CPRs), which are often not perfectly known. Recent research has found that the Josephson diode effect (JDE) can be related to the high harmonic content of the current-to-phase relation of the weak links embedded in superconducting interferometers. This makes the JDE a natural tool for exploring the harmonic content of weak links beyond single-harmonic CPR. In this study, we present the theoretical model and experimental characterization of a double-loop superconducting quantum interference device (DL-SQUID) that embeds all-metallic superconductor-normal metal-superconductor junctions. The proposed device exhibits the JDE due to the interference of the supercurrents of three weak links in parallel, and this feature can be adjusted through two magnetic fluxes, which act as experimental knobs. We carry out a theoretical study of the device in terms of the relative weight of the interferometer arms and the experimental characterization concerning flux tunability and temperature.
A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents I1{I}_{1}I1​ and I2{I}_{2}I2​, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current I2{I}_{2}I2​ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current I1m{I}_{1m}I1m​(\ensuremath{\varphi}). For values of I2{I}_{2}I2​>Ic{I}_{c}Ic​ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.