Microwave superconductivityPart 1: History, properties and early applications

Martin NisenoffM. Nisenoff Associates, 1201 Yale Place, Suite #1004

Minneapolis MN 55403-1958

Abstract— The 100th anniversary of superconductivity will becelebrated during 2011. As part of this celebration, a SpecialSession has been scheduled for IMS 2011 to commemorate thisevent and highlight the potential impact of superconductivity onelectronic technologies, especially in the microwave and terahertzfrequencies regimes. In this paper, Part 1, the history, propertiesand some early high frequency applications of superconductivitywill be reviewed, while in Part 2, current and future applicationswill be discussed.

Index Terms— superconducting microwave devices, SQUIDs,superconducting filters, analog-to-digital convertors sensors,high-speed electronics, high temperature superconductors

I. INTRODUCTION

On 8 April 1911, in the Physical Laboratory of the LeidenUniversity in Leiden, The Netherlands, Prof Heike KamerlinghOnnes and his collaborators, Cornelis Dorsman, Gerrit JanFlim, and Gilles Holst, were studying the electrical propertiesof pure materials in the temperature range near 4 kelvin, thetemperature of liquid helium at atmospheric pressure. As thetemperature of a pure mercury sample was lowered toward3 kelvin, they observed that the resistance became “practicallyzero”. In a subsequent experiment on 23 May 1911, theycooled a mercury sample to 3 kelvin and again observed thatthe resistance was “practically zero”. As the temperature ofthe sample was slowly raised, near 4 kelvin, the resistanceabruptly increased, by more than three orders of magnitudeover a temperature interval much less than 0.1 kelvin. Thisnew phenomena was initially called “supraconductivity” butwas later change to “superconductivity” [1].

To recognize the importance of this discovery to electricaltechnology and to commemorate the 100th anniversary of thediscovery of superconductivity by Prof. Kamerlingh Onnesand his collaborators, the IEEE has designated the event asa Milestone in Electrical Engineering and Computing anda Milestone Plaque was dedicated on 8 April 2011 in thebuilding where the experiments were performed. See Fig.1 [2].

In connection with the celebration of the centennial ofsuperconductivity, and the dedication of the IEEE MilestonePlaque, a Special Historic Session has been organized for IMS2011 to provide an overview of the history of superconduc-tivity and its unique properties will be briefly reviewed andrelated to many of the existing applications of superconduc-tivity, especially at microwave and terahertz frequencies andspeculations offered on other potential applications [3], [4],[5].

Fig. 1. Photograph of Milestone Plaque that was dedicated at thesite where superconductivity was discovered.

II. A BRIEF HISTORY OF SUPERCONDUCTIVITY

For the first 50 years after its discovery, superconductiv-ity remained a very exotic phenomenon. In the late 1950s,John Bradeen, Leon Cooper and Robert Schrieffer proposeda theory, [6], which is commonly referred to as the “BCStheory” which described, in great detail, the unique electricaland thermal properties of the superconducting state. For theirpioneering work in developing their theory, they received theNobel Prize in Physics in 1972.

During the first 75 years after the discovery of supercon-ductivity in mercury, more than 5,000 elements, compoundsand alloys were discovered to exhibit superconductivity attemperatures below about 23 K, including about one-half ofthe elements. In 1986, Bednorz and Mueller [7] discovereda class of oxide materials which were superconducting attemperatures above 23 K and other materials have beendiscovered subsequently with transition temperatures as highas 150 K. These materials can significantly reduce the cryo-genic burden associated with the use of superconductors asthese materials can be operated at temperature near and evenabove 77 K, the temperature of boiling liquid nitrogen atatmospheric pressure. Unfortunately, these “high temperaturesuperconductors” (HTS) tend to be ceramic in nature and thusare relatively difficult to fabricate into useful configurations,such as cables and conductors. There are a large number ofbooks and articles in the open literature that describe thestatus of both “low temperature superconductors” (LTS) and

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HTS materials, per se, and the status of fabricating thesematerials into useful conductors and eventually into practicalapplications.

III. PROPERTIES OF THE SUPERCONDUCTING STATE

There are a number of very unique properties of thesuperconducting state that enable the development of appli-cations that cannot be realized using conventional electricaltechnologies.

1) Critical Temperature: The most commonly known prop-erty of the superconducting state is that a superconductoris characterized by a critical temperature, below which thematerial exhibits “zero” resistance. In the original experimentson mercury, the upper limit to the resistivity of mercury in thesuperconducting state was estimated to be about 10−6 that ofthe resistance at room temperature.

2) Persistent Current: If a current is induced in a totallysuperconducting loop, the current will continue to flow “indef-initely” as long as the sample remains in the superconductingstate. Recent experiments on superconducting magnets oper-ated with the terminals “superconductively shorted together”have shown that if the current did decay, the decay time wouldbe something like 150,000 years corresponding to resistivityof less than 10−22 ohm-cm, which is at least 16 ordersof magnitude smaller than the resistivity of copper at roomtemperature.

3) Critical Magnetic Field: A superconductor, at a tem-perature below the critical temperature, will remain in thesuperconducting state provided that the sample is not exposedto a magnetic field above a “critical” value, characteristic ofthe particular superconductor, which depends on temperature,it is zero at (and above) the critical temperature and slowlyincreases as the temperature is lowered below the criticaltemperature.

4) Critical Current Density: A superconducting sample, ata temperature below the critical temperature, can carry a DCcurrent without resistance up to some critical current density,above which the sample will revert to the normal (resistive)state. While the critical temperature and the critical magneticfield are characteristics of the material, the critical currentdensity for a sample is very sensitive to the physical andmetallurgical state of the sample.

5) Magnetic Flux Exclusion: When a superconductor isplaced in a magnetic field, the magnetic field is excluded fromthe interior of the sample, except for a small surface regioncharacterized by a “penetration depth”. This effect is calledthe “Meissner Effect” after one of the discoverers [8].

6) Magnetic Flux Quantization: If a magnetic field doespenetrate into a superconductor, for example in the case of aloop of superconductor, the magnitude of the magnetic fieldsurrounded by the superconductor will be quantized in unitsof h/2e where h is Plancks constant and e is the charge on theelectron. This unit of magnetic flux is known as the “magneticflux quantum”.

7) Josephson Junction: A Josephson junction [9] consistsof two superconducting specimens separated by a barrierregion which can be an insulator, a conductor or anothersuperconductor where the “barrier” which controls the mag-nitude of the superconducting current flowing between thetwo superconductor “electrodes” depends on the dimensionsand electrical properties of the “barrier” between the twoelectrodes. The very non-linear characteristic of a Josephsondevice can be used as a detector or mixer of radiation in themicrowave, terahertz and infrared frequency regions of thespectrum, as a variable inductor in electrical circuits and as avery low power dissipation, very high speed switch in digitalcircuits. Furthermore, the Josephson junction is the basis forthe currently accepted International Voltage Standard.

8) Superconducting Energy Gap: According to the BCStheory, the Cooper pairs are bound together with an energy∆E given by the relationship

∆E = hν = 3.52kBTc (1)

where h is Plancks constant (h = 6.6262 × 10−34 Joule-sec), ν is the frequency, kB is Boltzmann constant (kB =1.3806× 10−23 Joules/Kelvin) and Tc is the superconductingtransition temperature. The photon frequency corresponding tothe energy gap of a superconductor with a Tc = 1 K is about73 GHz. Thus the energy gap of most superconductors cor-responds to photons in the terahertz or far infrared frequencyregions of the spectrum.

9) Electrical Losses at Finite Frequencies: The resistanceof a superconductor is “zero” only at DC. For frequencies, f ,much smaller than that corresponding to the energy gap, theresistance of a superconductor is given by the BCS theory as:

RBCS ≈(2πf)2

Texp(−1.76

T

Tc). (2)

For frequencies much greater than that corresponding tothe energy gap, the superconductor behaves like a normalconductor with the customary square root of the frequencydependence for the resistivity. For more detailed informationabout these properties of the superconducting state, the readershould consult some of the standard references given at theend of this manuscript [10].

IV. APPLICATIONS OF SUPERCONDUCTIVITY AT HIGHFREQUENCY FIELDS

In exploiting the unique properties of superconductivity forhigh frequency applications, the properties most commonlyused are the (near) “zero” resistance of superconductors atfinite frequencies and the nonlinear properties of the Joseph-son Effect. Other properties employed include magnetic fluxquantization and the (abrupt) transition from the normal to thesuperconducting state at “zero” frequency. The critical currentdensity is another important parameter as it is a measure ofthe maximum power that the device can transport.

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Fig. 2. Schematic representation of attenuation (upper trace) anddispersion (lower trace) for a niobium stripline transmission line asfunction of frequency. Note that, in the lower trace of Fig. 3, the phasevelocities for signals of different frequencies propagating down a su-perconducting transmission line is constant, independent of frequency(at least, for frequencies less than 0.1 of the frequency correspondingto the energy gap) and, hence, superconducting transmission lines aredispersion free!

A. Band Pass and Band Reject Filters

The most common application of superconductivity at highfrequencies is the construction of bandpass and band rejectfilters. In general the Q-value of the filter structures dependon the volume of the devices with higher Q-values requiringa larger volume: 3-dimensional resonators tend to have highQ-value and large volume while thin film resonators are muchsmaller in size with noticeably smaller Q-values. Thus, sincethe resistive losses for a superconductor at finite frequenciesare much less than that of a normal metal device of the samegeometry, filters and resonators are an attractive applicationopportunity for superconductors.

One of the earliest reported research on thin film supercon-ductor microwave filter structures was in 1971 when DiNardoet. al. [11] reported on thin lead ring resonators and halfwave length resonators operating at 14 GHz which exhibitedunloaded Q-values of about 200,000 at 4 K and about 500,000at 1.8 K. These values of Q are extremely difficult to realizeusing normal conducting materials, even for structures withvery large physical dimensions.

Despite the very impressive Q-values obtained for thesedevices, little subsequent work on thin film microwave res-onant devices operating at 4 K were reported until recently,when projects have started using high-Q, low loss microwave

Fig. 3. Photograph of lead thin film ring and half-wavelengthresonators on sintered alumina substrates. Length of the housing wasapproximately 2.5 cm [11].

Fig. 4. 9-cell niobium cavity assembly, approximately 1 meter inlength, which operates at frequencies near 1.3 GHz for possible use inthe International Linear Collider that would operates at temperaturesnear 1.8 K. Photograph courtesy of KEK, Japan.

resonators in the readout circuits of Transition Edge Sensors(TES) devices and for Quantum Computing applications.These specific applications will be addressed by other papersin this Special Session.

Although there was only little interest in thin film supercon-ductor resonant circuits at 4 K, there has been a strong interestin 3-dimensional resonant cavities by the high energy physicscommunity. Superconducting 3-dimensional radio frequency(RF) and microwave frequency resonators are commonly usedin High Energy particle accelerators, such as the Large HadronCollider (LHC) operating at CERN in Europe, to accelerate theparticles. The cavity geometry that is used has a path wherethere is a very high electric field gradient along which thebeam can be passed to give the particles an energy increaseas it circulated around the accelerator. Since these cavities areoperated at very high power, a very high Q implementation isessential to minimize the thermal heat load on the refrigerationsystem used to provide the required cryogenic environment forthese cavities. Superconductivity is the only known technologythat can provide the very high Q-values required for thisapplication!

Fig. 4 is a picture of a 9 cell niobium cavity operatingat 1.3 GHz designed for the International Linear Collider(ILC) which is proposed as the next generation of high energyparticle accelerators [12]. The unit is about 1 meter in lengthand when operated at 1.8 K exhibits a Q-value in excess of1011!

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B. Josephson Junction Devices

A Josephson Junction is a device consisting of two su-perconducting electrode separated by a “barrier” which canbe an insulator, a normal metal, a superconductor with alower transition temperature than the electrodes, or, even, adimensional constriction in the direction of current flow. Thecurrent, i, flowing through such a devices is given by theJosephson theory to be

i = i0sin

(2π

φ

φ0

)(3)

where i0 is the maximum value of the supercurrent that canflow through the devices before a voltage appears across thestructure, φ0 is the magnetic flux quantum (2.07× 10−15 We-bers) and φ is the magnetic flux threading the barrier region.Since magnetic flux is given by

φ =∫V dt, (4)

it is obvious that the I vs. V characteristic of a Josephsonjunction is extremely non-linear. This non-linear behavior hasbeen used to fabricate very sensitive mixers and detectorsof microwave and terahertz radiation and, until the recentdevelopment of cryogenically cooled semiconductor InP FETdevices; superconductor SIS devices were the preferred tech-nology for radio astronomy applications in the microwavefrequency regime. The non-linear I-V characteristics havealso been employed as a non-linear inductor for the sensitiveelement in parametric amplifiers with noise temperatures wellbelow 1 K for 4 K operation. Although it is not quiteso obvious, the very non-linear response of the Josephsondevice to radiation has been used to construct the internationalaccepted Voltage Standard which has demonstrated a precisionof better than 1 parts per billion.

When a current less than the critical current i0, is flowingthrough a Josephson device in the superconducting state, ifthe impressed current is increased above i0, or if a magneticfield is applied to the devices which will suppress the criticalcurrent the device will switch into the normal (resistive) stateat a time corresponding to a frequency greater than 775 GHzwhere the power dissipated by the device (in the normal state)is much less than a microwatt! This fast switching speed forthe Josephson device has lead to a family of very high-speeddigital and mixed signal devices. Analog-to-digital convertersoperating with clock frequencies in the 40 GHz range (andcapable of even higher clock speeds) have been demonstratedto date which can digitize signals well into the microwavefrequency range. These circuits employ the movement ofmagnetic flux quanta around the circuit and therefore, thistechnology inherently has extremely high precision as the “unitof information” is quantized [13]. A paper in this SpecialSession will address the use of Josephson digital devices toproduce mixed signal circuits operating at clock frequenciesup to and greater than 50 GHz. If these superconductor mixedsignal circuits can be built with sufficiently high sensitivities,they can be placed directly behind the antenna and the signal

could be immediately digitized without the use of analog pre-amplifiers which can introduce noise and distortion into thesignal. [14]

V. SUMMARY

The 100th anniversary of the discovery of superconduc-tivity is being observed in 2011 and a Historic Sessionhas been organized for IMS 2011. There are many veryunique properties of superconductivity that can be used tomake electrical and electronic devices with properties andcharacteristics that are, in many cases, impossible to achieveusing non-superconducting technologies. In this paper, a briefoverview of the history of superconductivity was presentedalong with a brief review of the properties of superconductivitythat can be used in high frequency devices and circuits. Someof the earlier attempts to use superconductivity in microwaveapplications were outlined. In the following paper, additionalapplications of microwave superconductivity will be described,especially those employing high temperature superconductorswhich were discovered in 1986. Other papers in this SpecialSession, will describe some additional research thrusts inmicrowave superconductivity.

REFERENCES

[1] D. van Delft and P. H. Kes, “The discovery of superconductivity,”Physics Today, vol. 63, no. 9, pp. 38–43, September 2010.

[2] Milestones: IEEE milestones program. IEEE Global Hystory Network.[Online]. Available: http://www.ieeeghn.org/wiki/index.php/Milestone-Nomination DISCOVERY OF SUPERCONDUCTIVITY 1911

[3] T. van Duzer and C. W. Turner, Principles of Superconductive Devicesand Circuits. New York, NY: Elsevier North Holland, 1981.

[4] M. Tinkham, Superconductivity. New York, NY: Gordon & Breach,1965.

[5] R. R. Mansour, “Microwave superconductivity,” IEEE Trans. MicrowaveTheory and Tech., vol. 50, no. 3, pp. 750–759, March 2002.

[6] J. Bardeen, L. N. Cooper, and J. R. Schreiffer, “Theory of superconduc-tivity,” Phys. Rev., vol. 108, no. 5, pp. 1175?–1204, 1957.

[7] I. G. Bednorz and K. A. Mueller, “Possible high-Tc superconductivityin Be-La-Cu-O system,” Zeit. fuer Phys., vol. B64, no. 2, p. 189?191,1986.

[8] W. Meissner and R. Ochsenfeld, “Ein neuer effekt bei eintritt dersupralaitfahigkeit,” Naturwissenschaften, vol. 21, no. 44, pp. 787–789,1933.

[9] B. D. Josephson, “Possible new effect in superconductive tunneling,”Physics Letters, vol. 1, no. 7, pp. 251–253, 1962.

[10] “Special issue on applications of superconductivity,” in Proceedings ofthe IEEE, T. van Duzer and W. V. Hassenzahl, Eds., vol. 92, no. 10,October 2004.

[11] J. G. S. A. J. Dinardo and F. R. Arams, “Superconducting microstriphigh-q microwave resonators,” J. Appl. Phys., vol. 42, no. 1, pp. 186–198, 1971.

[12] International linear collider. [Online]. Available:www.interactions.org/imagebank/search detail.php?image no=KE0116

[13] D. E. Kirchenko, T. V. Filippov, and D. Gutpa, “Microwave receiver withdirect digitization,” in Proc. IEEE MTT-S Int. Microw. Symp. Digest,2009.

[14] D. Gupta, “Superconductor analog-to-digital converters and their ap-plications,” Proc. IEEE MTT-S International Microwave SymposiumDigest, 2011.

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