Nanoscale Superconducting Quantum Interference Devices Add Another Dimension John Gallop* and Ling Hao National Physical Laboratory, Teddington TW11 0LW, United Kingdom ABSTRACT: Over the past decade, nanoscale superconducting quantum interference devices (nanoSQUIDs) have rapidly risen from nowhere to forge a new sphere of applications of these macroscopic quantum devices. New fabrication techniques have enabled these advances. In this Perspective, we highlight another recent major development in this areathe demonstration of a three-axis nanoSQUID magnetometer, which enables the vector magnetization of a nanoscale magnetic particle to be measured in the presence of an applied magnetic field. We illustrate the technological demands and developments that have driven the development of nanoSQUIDs and make suggestions for future directions for applications.
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electromagnetic potential, the (non) observation of free magnetic monopoles, the sign of the positron mass, and frame dragging in general relativity, to name just a few. They also became an important staple of metrology institutes, which relied on SQUIDs for realizing quantum electrical standards, including the Josephson volt and the quantum Hall effect resistance standard. As the strengths and weaknesses of this new scientific tool became apparent, development began to settle down. Superconducting quantum interference devices became available commercially. All-purpose cryogenic materials characterization systems based on SQUIDs entered general laboratory use, and specialized systems consisting of hundreds of SQUID devices (arranged in a cryogenic helmet) have come into widespread use for neuroimaging in hospitals. Toward the Nanoscale. Beginning around the turn of the millennium, these macroscopic quantum devices have taken on a new lease on life as SQUIDs began to shrink to the nanoscale. NanoSQUIDs were almost unheard of in the scientific literature before 1995. There has been explosive growth in research and the number of research publications in this area since then. In fact, it was appreciated much earlier2 that microscale SQUIDs were potentially useful as susceptometers for magnetic measurements on single magnetic nanoparticles (MNPs). However, the fabrication requirements were not generally available to provide truly nanoscale devices that would be able to operate in the high-magnetic fields required to investigate the magnetization loops of tiny magnetic particles. The breakthroughs that facilitated recent developments required a kind of rediscovery of “retro-SQUID” technology. To recap, when SQUIDs first appeared, the Josephson junctions that they incorporated were made from a wide
t is a truism that old ideas reappear in newly minted forms. Superconductivity (the complete loss of electrical resistance below a transition temperature, Tc) is hardly new, having been known for over a century. The macroscopic quantum nature of superconductivity was first elucidated and then exploited as long as 50 years ago. Superconductivity features in our everyday lives, from magnetic resonance imaging scanners to high-energy accelerators, but there are still new areas to research and to exploit. At present, a hot topic is the reinvention of superconducting electronics by taking to the nanoscale. History of Superconducting Quantum Interference Device Development. Back in the 1960s, when our understanding of the nature of superconductivity as a solidstate phase transition had greatly increased, the first superconducting quantum interference devices (SQUIDs) were made. Their appearance followed rapidly from the prediction and observation of magnetic flux quantization in superconductors and the theoretical prediction of the Josephson effects. At its most basic, a SQUID consists of a loop of superconducting wire interrupted by one or more Josephson junctions. The loop of superconductor quantizes the magnetic flux linking it, in units of ℏ/2e (where ℏ is Planck’s constant and 2e is the electrical charge of an electron pair). The Josephson junctions in a SQUID enable single magnetic flux quanta to be manipulated, and the small size of the quantum (Φ0 = ℏ/2e = 2 × 10−15 Wb) makes these devices very sensitive magnetic field detectors. For an encyclopaedic discussion of SQUIDs, the theory underlying their operation as well as their widespread applications see ref 1. In the 1970s, the first SQUIDs moved from being quantum curiosities in research laboratories to making profound impact across basic physics and influencing our understanding of the nature of the Published XXXX by the American Chemical Society
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processes are used to remove unwanted superconducting film, leaving a bridge with similar minimum dimensions to that achievable with FIB, but without the possible contamination from implanted ions. Perhaps the most exotic and impressive technique involves evaporating a superconducting film on the end of a drawn down pipet tube, a cunning approach that requires no lithographic step but has produced the smallest SQUIDs so far, a loop just 100 nm across and junctions with lengths of perhaps only 30 nm.8 The process of scanning probe anodization, however, has not yet been explored for nanoSQUIDS. The development of microprobe techniques in the 1990s, such as scanning tunnelling microscopy (STM) and atomic force microscopy (AFM), raised the hope that these methods could be used to prepare sub-10 nm features in thin films by removing material just in the region of a probe tip as it is scanned. Demonstration devices have been made, but as yet the yield and performance are not impressive.9 For a recent, detailed description of the nanoSQUID stateof-the-art see ref 10.
variety of different types of superconducting weak links, including atomically thin tunnel barriers between thin-film superconductors, nanowire constrictions, normal metal barriers between superconductors, and dry-joints between a blob of solder and a superconducting wire. All of these devices showed interesting and useful performance but suffered from the inability to be scalable or even reliably fabricated. Finally, in the 1980s, a truly scalable trilayer Josephson tunnel junction process was invented, which enabled reproduction of many nearly identical Josephson junctions at the same time. Superconducting foundries grew up, able to manufacture reliable SQUIDs by the thousand on a single chip, and this fabrication technology became the industry norm.3 However, this manufacturability did not enable nanoscale devices. The primary reason was that the critical currents that tunnel junction SQUIDs could achieve were too small to make low-noise devices when scaled down below 1 μm. Instead, early nanoSQUIDs relied on an old and mainly discarded technology in which the junction is made from a narrow and short superconducting wire connecting the two superconductors, a so-called Dayem bridge junction. These junctions have much higher critical current densities than insulating tunnel barrier junctions but also lower capacitance, which helps with improving both the low-noise performance and high-frequency properties. Fabrication Methods. The present nanoSQUID situation is a kind of “Cambrian explosion” era of Josephson junction types, echoing what was seen back in the 1970s when novel ideas for SQUIDs first proliferated. The new generations of nanojunctions are also made using a plethora of different methods. The first and perhaps simplest is focused ion beam (FIB) milling, in which a low-melting-point metal, typically Ga, provides an energetic beam of highly focused massive ions, which is steered across a predeposited thin film of superconductor, removing material according to a preprogrammed pattern. In this way,4,5 Dayem bridges with typical dimensions as small as 50 nm in length by 50 nm in width and thickness can be produced quickly and reliably (see Figure 1). A second method6,7 is the well-established electron-beam lithography (EBL) process, which is more complex than FIB and relies on polymer-based resist methods, layers of which are spun on to the superconducting film, then exposed by a rastered, finely focused e-beam. Finally, wet or dry etching
A fourth junction fabrication technique comes closest to establishing an allpurpose method for nanoSQUID pró duction and is described by MartinezPérez et al. in this issue of ACS Nano.
THREE-DIMENSIONAL (3D) NANOSQUID MAGNETOMETER ́ The paper by Martinez-Pé rez et al.9 shows a considerable advance on what has previously been achieved with nanoSQUIDs. Although the SQUID loops are not as small as have been realized elsewhere, the key development is the ability to integrate three orthogonal loops in the single device, each loop with two Josephson junctions and including all necessary control lines. The 3D SQUID system uses a type of Josephson device that is intermediate between tunnel junctions and Dayem bridges, namely a superconductor-normal metal-superconductor (SNS) junction, based on a Nb/HfTi/Nb sandwich. Replacing the traditional insulating tunnel barrier in a Josephson junction with a thin, normal (i.e., nonsuperconducting) metal layer provides a much greater critical current density, enabling the junction cross-sectional area to be correspondingly reduced. To achieve accuracy and reproducibility with features down to tens of nanometers, high-precision EBL is used, combined with chemical−mechanical polishing. The complexity of the structure is epitomized by the scanning electron microscopy (SEM) image of the device (Figure 2). The three orthogonal SQUID loops have areas from 500 × 500 nm (for the loop in the plane of the substrate) to more slot-shaped loops (600 × 90 nm). The vertical separation of the x and y loops is set by evaporated film thickness. The junctions themselves are around 100 nm square. Below the larger loop is a superconducting hairpin-shaped track that can apply a magnetic field to only half of the z-axis loop, in order to provide an element of gradiometric response. Control lines for the other two axes are provided by superconducting tracks of the SQUID loops themselves.
Figure 1. Atomic force microscopy image of FIB milled niobium nanoSQUID with two Dayem bridge junctions. Reprinted from ref 4. Copyright 2007 American Chemical Society. B
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these NMPs, preventing full 3D analyses of the magnetic response from a disordered group of particles. If the NMPs are not widely dispersed, then the interactions between them will be strong enough to obscure the properties of a single particle. ́ The 3D magnetometer described by Martinez-Pé rez et al. gets around this issue and is capable of characterizing single particles as small as 100 nm. These particles are of great interest for magnetic storage and spintronics as well as for magnetic biotags.
FURTHER MINIATURIZATION? How will nanoSQUIDs develop further? It is hard to see how conventional nanoSQUID designs could shrink by more than a factor of 10. There is a seeming convergence of fabrication methods, with the FIB microbridges still maintaining a small advantage over the SNS junction methods, while progress with the lithography-less tip junction methods have the smallest size and best spin detection level (in one direction only) at present (see Figure 3). With further incremental refinement we may expect junction sizes to approach 10 nm in size using any of the above fabrication methods. However, the need to apply flux bias to each SQUID loop requires control lines to be placed in close proximity to the loops and an interesting limit is approaching from this direction. It is perhaps surprising to realize that for a SQUID loop 100 × 100 nm (at the lower limit of what is currently attainable), the magnetic flux density corresponding to a single flux quantum within it is as high as 0.2 T. This is a modest field to apply using a multiturn superconducting coil, but it is problematic to apply a field of this magnitude using a local current-carrying control line. As an example, consider a conductor strip at a distance a from a loop of length L and width w parallel to it. The current I through it required to apply one flux quantum to the loop (approximately the minimum required to optimize the operating SQUID condition) is set by the approximate expression:
Figure 2. (a) Schematic view of the three-axis nanoSQUID magnetometer, consisting of three mutually orthogonal nanoloops. The external magnetic field H is applied along the z-axis. (b) Scanning electron micrograph of a typical device (false color). Yellow dashed squares indicate the position of the Josephson junctions. Black solid and dashed arrows indicate the direction of bias currents Ib and modulation currents Imod, respectively. Reprinted from ref 9. Copyright 2016 American Chemical Society.
A key question is the orthogonality of the three axial loops, i.e., to what extent a magnetic signal along one axis couples to either of the other two axes at right angles. Even if the geometric orthogonality is perfect, the finite cross-section of the wiring tracks will cause distortion of applied magnetic fields due ́ to the Meissner effect. An important result from MartinezPérez et al. is that this orthogonality was experimentally tested and found to be surprisingly good, opening the way for the measurement of the full anisotropic response of any MNP which is positioned within the SQUID system.
I=
aℏ 4eμ0 wL
Given that a and w are approximately equal in a favorable case, and for a true nanoscale loop L < ∼100 nm, this requires that I > 10 mA. This may seem a relatively modest current, but it is by no means easily achieved even through a track that is superconducting, if it is only 10 nm wide and approximately the same thickness. This requires a current density of 1014 A/ m2, close to the critical value for good metallic superconductors such as pure Nb. Further significant reductions in loop size will demand more complex solutions to the control line problem, perhaps requiring flux focusing structures that would greatly add to fabrication complexity.
́ ́rez et al. is a The paper by Martinez-Pe major development toward the nanoscale application of a SQUID magnetometer system.
ULTIMATE SYSTEMS Over the first decade of nanoSQUID existence, a great deal of ́ development has occurred, and the paper by Martinez-Pé rez et al. in this issue of ACS Nano9 is an excellent example of the present state of maturity. However, many issues remain to be solved before the ultimate performance can be reached, for which the smallest junctions must exhibit close to ideal properties. For conventional SQUID operation, the device is biased by a direct current (DC) beyond its critical current where the variation of DC voltage with changes in applied flux dV/dΦ is a maximum. The normal state resistance, R, of the junctions must be as high as possible, while maintaining a large
STATE-OF-THE-ART A conventional commercial SQUID magnetometer can measure the susceptibility of modest amounts (down to micrograms) of magnetic material at temperatures up to, or even above, room temperature at magnetic fields up to some 5−10 T. However, there is much interest in measuring small magnetic particles down to micrometers in size or even below. Conventional systems can only measure large ensembles of C
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Figure 3. (a) Scanning electron micrograph of the smallest nanoSQUID to date8 grown on a drawn-down quartz tip. (b) Spectral density of the SQUID noise, in terms of Bohr magnetons (μB) in unit bandwidth. Reprinted with permission from ref 11. Copyright 2013 Nature Publishing Group.
Figure 4. Images of single-layer Dayem bridge nanoSQUIDs. (a) nanoSQUID with 100 nm NMP positioned on edge of loop. Reprinted with permission from ref 14. Copyright 2015 IEEE. (b) AFM image of slot-shaped SQUID with 0.1 μm2 loop area. Reprinted with permission from ref 15. Copyright 2015 IEEE. (c) Nanoelectromechanical system (NEMS) beam resonator positioned on top of slot-shaped nanoSQUID. Reprinted with permission from ref 14. Copyright 2015 IEEE.
resonant circuit, highly sensitive flux changes may be detected. This method of readout has the potential to improve the signalto-noise ratio over a conventional readout with DC bias into the resistive region of a SQUID’s current voltage characteristic. When so biased, the SQUID exhibits a normal-state resistance so that Nyquist noise voltage fluctuations will limit the SQUID sensitivity, whereas the inductive method is not hampered by this source of noise. In the low-power limit, the system is limited by the noise temperature of the microwave amplifier that follows the reflected signal, which may be higher than that of a room-temperature audio amplifier. However, the inductance of the SQUID loop has been shown to be nonlinear with increasing microwave power, allowing parametric gain. For sufficiently high drive power levels, the increased gain overcomes the noise limitations of the following amplifier so that quantum-limited operation has been demonstrated at 50 mK12 and may become available at even higher temperatures. The smallest junctions thus far have been fabricated with the lithography-free tip process, but along with the FIB technique, these methods have a limitation in that the junctions can only operate over a relatively limited range of temperature since the critical currents are strongly temperature dependent. This issue can be solved if even smaller junctions can be madesmaller than the coherence length of the superconducting filmsthus preventing the development of phase slip centers within the junctions and extending the operating temperature range.
critical current, i.e., maximizing the product icR. Fundamental theories predict that the maximum value is not greater than the energy gap of the superconducting material from which the junction lands are made. For Nb, this value of icR is ∼1.8 mV and FIB-created microbridges already achieve close to this value; dV/dΦ values as high as 2 mV/Φ0 have been achieved. The flux signal resulting from flipping a single electronic spin for a nanoSQUID of this size amounts to around 10−6Φ0, which means that a single electronic flip could be detected by a nanoSQUID using a conventional room temperature amplifier with a value of R ∼ 10 Ω. Recent developments in SQUID detection also promise further improvements in sensitivity. There is a widespread assumption that SQUID devices, particularly analogue SQUID sensors, are low-frequency systems. In reality, Josephson junctions are sensitive to frequencies into the high microwave range and in fact are capable, through the alternating current (AC) Josephson effect, to generate microwave supercurrents. Microwave biased and interrogated SQUIDs have been known for many years, though little exploited. Recent developments, however, have shown how SQUIDs may be interrogated inductively, without ever being driven into their normal state, where the internal currents exceed the SQUID critical current. The microwave signal reflected from a SQUID has a phasedependent relationship to the driving current, which is fluxquantum periodic in the applied magnetic flux. If such a SQUID is incorporated into a superconducting microwave D
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Superconducting-Quantum-Interference Devices Fabricated by Focused Ion Beam. Appl. Phys. Lett. 2008, 92, 192507. (6) Lam, S. K. H.; Tilbrook, D. L. Development of a Niobium Nanosuperconducting Quantum Interference Device for the Detection of Small Spin Populations. Appl. Phys. Lett. 2003, 82, 1078−1081. (7) Wernsdorfer, W. From Micro- to Nano-SQUIDs: Applications to Nanomagnetism. Supercond. Sci. Technol. 2009, 22, 064013. (8) Anahory, Y.; Reiner, J.; Embon, L.; Halbertal, D.; Yakovenko, A.; Myasoedov, Y.; Rappaport, M. L.; Huber, M. E.; Zeldov, E. ThreeJunction SQUID-on-Tip with Tunable In-Plane and Out-of-Plane Magnetic Field Sensitivity. Nano Lett. 2014, 14, 6481−6487. (9) Martínez-Pérez, M. J.; Gella, D.; Müller, B.; Morosh, V.; Wölbing, R.; Sesé, J.; Kieler, O.; Kleiner, R.; Koelle, D. Three-Axis Vector Nano Superconducting Quantum Interference Device. ACS Nano 2016, DOI: 10.1021/acsnano.6b02218. (10) Granata, C.; Vettoliere, A. Nano Superconducting Quantum Interference Device: A Powerful Tool for Nanoscale Investigations. Phys. Rep. 2016, 614, 1−69. (11) Vasyukov, D.; Anahory, Y.; Embon, L.; Halbertal, D.; Cuppens, J.; Neeman, L.; Finkler, A.; Segev, Y.; Myasoedov, Y.; Rappaport, M. L.; Huber, M. E.; Zeldov, E. A Scanning Superconducting Quantum Interference Device with Single Electron Spin Sensitivity. Nat. Nanotechnol. 2013, 8, 639−644. (12) Hatridge, M.; Vijay, R. D.; Slichter, H.; Clarke, J.; Siddiqi, I. Dispersive Magnetometry with a Quantum Limited SQUID Parametric Amplifier. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 134501. (13) Hao, L.; Aßmann, C.; Gallop, J. C.; Cox, D.; Ruede, F.; Kazakova, O.; Josephs-Franks, P.; Drung, D.; Schurig, T. Detection of Single Magnetic Nanobead with a Nano-Superconducting Quantum Interference Device. Appl. Phys. Lett. 2011, 98, 092504. (14) Hao, L.; Cox, D.; Gallop, J. C.; Chen, J. Fabrication and Analogue Applications of NanoSQUIDs Using Dayem Bridge Junctions. IEEE J. Sel. Top. Quantum Electron. 2015, 21, 9100108. (15) Bechstein, S.; Ruede, F.; Drung, D.; Storm, J.-H.; Köhn, C.; Kieler, O. F.; Kohlmann, J.; Weimann, T.; Patel, T.; Li, B.; Cox, D.; Gallop, J. C.; Hao, L.; Schurig, T. Design and Fabrication of Coupled NanoSQUIDs and NEMS. IEEE Trans. Appl. Supercond. 2015, 25, 1602604. (16) Boixo, S.; Rønnow, T. F.; Isakov, S. V.; Wang, Z.; Wecker, D.; Lidar, D. A.; Martinis, J. M.; Troyer, M. Evidence for Quantum Annealing with More than One Hundred Qubits. Nat. Phys. 2014, 10, 218−224. (17) Alsina, D.; Latorre, J. I. Experimental Test of Mermin Inequalities on a Five-Qubit Quantum Computer. Phys. Rev. A: At., Mol., Opt. Phys. 2016, 94, 012314. (18) Kane, B. E. A Silicon-Based Nuclear Spin Quantum Computer. Nature 1998, 393, 133−137. (19) Pla, J. J.; Tan, K. Y.; Dehollain, J. P.; Lim, W. H.; Morton, J. J. L.; Jamieson, D. N.; Dzurak, A. S.; Morello, A. A Single-Atom Electron Spin Qubit in Silicon. Nature 2012, 489, 541−545.
If nanoSQUIDs are to be used to analyze the properties of NMPs, it will be necessary to bring about a means for reliably and accurately delivering one to the other. Nanomanipulators can be used to position an NMP close to a SQUID loop or even bring a nanomechanical beam resonator in close coupling with a nanoSQUID (see Figure 4a,c, refs 13 and 14) but this is a relatively slow and tricky process. However, here is where scanned probe techniques should prove useful. A submicron single loop nanoSQUID, including all necessary wiring and control lines may, in principle, can be fabricated on a blunt AFM tip, and when mounted in a low-temperature AFM system, the piezoelectric motion and control of the AFM may be used to bring the SQUID to within nanometers of a selected NMP. The ability to use a 3D SQUID system in this way is a little more challenging. A means for bringing the NMP within the three-coil system would be required, but we expect that with ingenuity, researchers will be able to solve this tricky manipulation. The rapidly developing nanoSQUID technology may impact another exciting application, if the performance in terms of energy sensitivity can be improved by a further factor of 10− 100. Solid-state quantum information processing (QIP) is already a crowded area. Here, micrometer-scale trilayer SQUIDs are already leading contenders for true quantum computing applications.16,17 The ability to detect a single electronic or nuclear spin flip could be an enabling technology for single-spin-based QIP developments.8 Scalable nanoSQUID circuits can be produced, with each SQUID under independent ́ control through added lines as shown by Martinez-Pé rez et al.9 However, an additional critical facilitating technology is also on the horizon, namely precise positional “deterministic” implantation into a solid-state substrate of single dopant ions, with long-lived (electron or nuclear) spin states. At present, 31P implanted in Si or nitrogen vacancy states in diamond are favored. This wish list for QIP was first formulated by Kane,18 but it has taken almost 20 years to approach realization. It is now in sight,19 with location expected to within ∼10 nm. It seems we are set for another nanoSQUID revolution, bringing together single spins and macroscopic quantum objects in dense arrays. If this tour de force can be carried through, the scale of all previous applications of SQUIDs, of any size, will pale into insignificance.
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
REFERENCES (1) Clarke, J.; Braginski, A. I. The SQUID Handbook. Wiley-VCH Verlag GbmH & Co.: Weinheim, 2005, DOI: 10.1002/ 3527603646.fmatter. (2) Ketchen, M. B.; Kopley, T.; Ling, H. Miniature SQUID Susceptometer. Appl. Phys. Lett. 1984, 44, 1008−1010. (3) Barfknecht, A. T.; Ruby, R. C.; Ko, H. L. A Simple and Robust Niobium Josephson Junction Integrated Circuit Process. IEEE Trans. Magn. 1991, 27, 3125−3128. (4) Troeman, A. G. P.; Derking, H.; Borger, B.; Pleikies, J.; Veldhuis, D.; Hilgenkamp, H. NanoSQUIDs based on Niobium Constrictions. Nano Lett. 2007, 7, 2152−2156. (5) Hao, L.; Macfarlane, J. C.; Gallop, J. C.; Cox, D.; Beyer, J.; Drung, D.; Schurig, T. Measurement and Noise Performance of NanoE
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