Taming High-Temperature Superconductivity

CERN Courier September 2017 HTS theory

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TRACkS Prototype “Roebel” cable based on the high-temperature superconductor REBCO (rare-earth barium-copper oxide) is being used to 600 Abstracts accepted! Experiment control wind a demonstration accelerator dipole at CERN as part of the EuCARD-2 project. (Image credit: H Barnard/CERN.) Online registration is open Functional safety & machine protection Software technology evolution Put simply, superconductivity is the ability of a system of User Interfaces & User Experience (Ux) ENDORSED BY Understanding the mechanism behind Project status reports fermions to carry electric current without dissipation. Normally, Control system upgrades high-temperature superconductivity, fermions such as electrons scatter off any obstacle, including each Data management & processing other. But if they find a way to form bound pairs, these pairs may Integrating diverse systems discovered three decades ago, is a major condense into a macroscopic state with a non-dissipative current. It infrastructure for control systems Feedback control & process tuning theoretical challenge that has the potential to Quantum mechanics is the only way to explain this phenomenon, Hardware technology but it took 46 years after the discovery of superconductivity for timing & synchronization ORGANIZER Bardeen, Cooper and Schrieffer (BCS) to develop a verifiable Systems engineering, collaborations & impact other fields including particle physics. project management theory. Winning the 1972 Nobel Prize in Physics for their efforts, Data analytics they figured out that the exchange of phonons leads to an effec- Superconductivity is perhaps the most remarkable manifestation of tive attraction between pairs of electrons of opposite momentum quantum physics on the macroscopic scale. Discovered in 1911 by if the electron energy is less than the characteristic phonon energy Kamerlingh Onnes, it preoccupied the most prominent physicists (figure 1, overleaf). Although electrons still repel each other, the of the 20th century and remains at the forefront of condensed- effective Coulomb interaction becomes smaller at such frequen- matter physics today. The interest is partly driven by potential cies (in a manner opposite to asymptotic freedom in high-energy applications – superconductivity at room temperature would physics). If the reduction is strong enough, the phonon-induced surely revolutionise technology – but to a large extent it reflects an electron–electron attraction wins over Coulomb repulsion and the 16th International Conference on intellectual fascination. Many ideas that emerged from the study total interaction becomes attractive. There is no threshold for the Accelerator and Large Experimental of superconductivity, such as the generation of a photon mass in magnitude of the attraction because low-energy fermions live at Physics Control Systems a superconductor, were later extended to other fields of physics, the boundary of the Fermi sea, in which case an arbitrary weak famously serving as paradigms to explain the generation of a Higgs attraction is enough to create bound states of fermions at some s www.icalepcs2017.org mass of the electroweak W and Z gauge bosons in particle physics. critical temperature, Tc.

CCSep17_HTSTHEORY.indd 43 02/08/2017 16:09 CERNCOURIER www. V o l u m e 5 7 N u m b e r 7 S e p t e m b e r 2 0 1 7 CERN Courier September 2017 CERN Courier September 2017 HTS theory HTS theory B Glowacki October 1993 pʹ HgBa2Ca2CU3O8-x March 1988 Woodstock physics Ti2Ba2Ca2Cu3O10-x (K)

January 1988 134 K p –p Bi2Sr2Ca2Cu3O10-x February 1987 LNG Tb = 112K 120 P Schewe & P Grant –pʹ YBa2Cu3O7 December 1986 (La, Ba)2CuO4 91 K pʹ under pressure December 1986 pʹ –pʹ LN2 Tb = 77.4K 80 (La, Sr)2CuO4 77 K April 1986 MgB2(40K) p –p (La, Ba)2CuO4 SmFeAsO (55K)

Nb12Al3Ge XC(60) V3Si Nb3Ge 39K NbC Nb3Sn 40 NbN LH Tb = 20K –pʹ Nb 2 p –p Hg Pb alloys and non-oxide compounds oxide ceramics metals ceramics LHe Tb = 4K organic 0 Participants at a special session of the 1987 March meeting of the Fig. 1. Pairing in a conventional superconductor involves an 1900 1920 1940 1960 1980 2000 2020 2040 A WO LiTi O κ-(ET) X electron (red) with momentum p scattering off a virtual phonon SrTiO3 λ 3 2 4 (TMTSF)2X 2 American Physical Society in New York devoted to the newly discovered (blue) to the state pʹ. The virtual phonon is extremely slow BaPb1-xBixO3 β-(ET)2X high-temperature superconductors. The hastily organised session, which compared with the electron, so another electron of momentum Fig. 2. Materials with record superconducting transition later became known as the “Woodstock of Physics” lasted from the early −p can scatter off the same phonon to state –pʹ. The net effect temperatures as a function of time, showing BCS evening to 3.30 a.m. the following morning, with 51 presenters and more (bottom line) is that two pairs of electrons with zero total superconductors, iron-based superconductors and than 1800 physicists in attendance. Bednorz and Müller received the momentum have scattered off one another and, since the high-temperature cuprate superconductors. The current record Nobel prize in December 1987, one year after the discovery, which was the electrons were not at the same place at the same time, they can holder is a BCS-type superconductor, hydrogen sulphide, under fastest award in the Nobel’s history. avoid the direct Coulomb repulsion. a gigantic pressure of 155 GPa (not shown).

The formation of bound states, called Cooper pairs, is one neces- Unconventional superconductors The cuprates hold the record for the highest Tc for materials with sary ingredient for superconductivity. The other is for the pairs to In the early 1980s, when the record critical temperature for super- an unconventional pair wave-function symmetry: 133 K in mercury-

condense, or more specifically to acquire a common phase corre- conductors was of the order 20 K, the dream of a superconductor based HgBa2Ca2Cu3O8 at ambient pressure. They were not, however, sponding to a single macroscopic wave function. Within BCS theory, that works at liquid-nitrogen temperatures (77 K) seemed far off. the first materials of this kind: a “heavy fermion” superconductor

pair formation and locking of the phases of the pairs occur simulta- In 1986, however, Bednorz and Müller made the breakthrough dis- CeCu2Si2 discovered in 1979 by Steglich, and an organic supercon-

neously at the same Tc, while in more recent strong-coupling theories covery of superconductivity in La1−xBaxCuO4 with Tc of around ductor discovered by Jerome the following year, also had an uncon- bound pairs exist above this temperature. The common phase of the 40 K. Shortly after, a material with a similar copper-oxide-based ventional pair symmetry. After the discovery of cuprates, a set of

pairs can have an arbitrary value, and the fact that the system chooses structure with Tc of 92 K was discovered. These copper-based unconventional iron-based superconductors was discovered with Tc Fig. 3. Atomic structure of one of the best-known high-temperature

a particular one below Tc is a manifestation of spontaneous sym- superconductors, known as cuprates, have a distinctive structure up to 60 K in bulk systems, followed by the discovery of supercon- superconductors, YBa2Cu3O7, showing the position of copper

metry breaking. The phase coherence throughout the sample is the comprising weakly coupled layers made of copper and oxygen. In ductivity with an even higher Tc in a monolayer of FeSe. But even (orange), oxygen (red), barium (green) and yttrium (blue) atoms.

most important physical aspect of the superconducting state below all the cuprates, the building blocks for superconductivity are the low-Tc, unconventional materials can be interesting. For example, The material is highly anisotropic and pairing occurs in the CuO2

Tc, as it can give rise to a “supercurrent” that flows without resistance. CuO2 planes, with the other atoms providing a charge reservoir that some experiments suggest that Cooper pairs in Sr2RuO4 have total planes. By removing oxygen far from the planes, one can change Superconductivity can also be viewed as an emergent phenomenon. either supplies additional electrons to the layers or takes electrons spin-one and p-wave symmetry, leading to the intriguing possibility the average number of conduction electrons. While BCS theory was a big success, it is a mean-field theory, out to leave additional hole states (figure 3). that they can support edge modes that are Majorana particles, which

which neglects fluctuations. To really trust that the electron– From a theoretical perspective, the high Tc of the cuprates is have potential applications in quantum computing. tively different from that in an ordinary metal (figure 4, overleaf). phonon mechanism was correct, it was necessary to develop theo- only one important aspect of their behaviour. More intriguing is If phonon-mediated electron–electron interactions are ineffective At zero doping, standard solid-state physics says that the system retical tools based on Green functions and field-theory methods, what mechanism binds the fermions into pairs. The vast major- for the pairing in unconventional superconductors, then what binds should be a metal, but experiments show that it is an insulator. and to move beyond weak coupling. The BCS electron–phonon ity of researchers working in this area think that, unlike low- fermions together? The only other possibility is a nominally repul- This is taken as an indication that the effective interaction between mechanism of superconductivity has since been successfully temperature superconductors, phonons are not responsible. The sive electron–electron interaction, but for this to allow pairing, the electrons is large, and such an interaction-driven insulator is called applied to explain pairing in a large variety of materials (figure 2), most compelling reason is that the cuprates possess “unconven- electrons must screen their own Coulomb repulsion to make it effec- a Mott insulator. Upon doping, some states become empty and the from simple mercury and aluminium to the niobium-titanium tional” symmetry of the pair wave function. Namely, in all known tively attractive in at least one pairing channel (e.g. d-wave). Inter- system eventually recovers metallic behaviour. A Mott insulator and niobium-tin alloys used in the magnets for the Large Hadron phonon-mediated superconductors, the pair wave function has estingly, quantum mechanics actually allows such schizophrenic at zero doping has another interesting property: spins of localised Collider (LHC), in addition to s-wave symmetry, or in other words, its angular dependence is behaviour of electrons: a d-wave component of a screened Coulomb electrons order antiferromagnetically. Upon doping, the long- the recently discovered sul- isotropic. For the cuprates, it was proven in the early 1990s that interaction becomes attractive in certain cases. range antiferromagnetic order quickly disappears, while short- The observation of phur hydrides, which become the pair wave function changes sign under rotation by 90°, lead- range magnetic correlations survive. superconductors at a tempera- ing to an excitation spectrum that has zeros at particular points Cuprate conundrums Since the superconducting region of the phase diagram is sand- d-wave symmetry ture of around 200 K under on the Fermi surface. Such symmetry is often called “d-wave”. There are several families of high-temperature cuprate super- wiched between the Mott and metallic regimes, there are two ways in the cuprates high pressure. But the dis- This is the first symmetry beyond s-wave that is allowed by the conductors. Some, like LaSrCuO, YBaCuO and BSCCO, show to think about HTS: either it emerges upon doping of a Mott insulator was extremely covery of high-temperature antisymmetric nature of the electron wave functions when the superconductivity upon hole doping; others, like NdCeCuO, show (if one departs from zero doping), or it emerges from a metal with superconductors drove con- total spin of the pair is zero. The observation of a d-wave sym- superconductivity upon electron doping. The phase diagram of increased antiferromagnetic correlations if one departs from larger surprising. densed-matter theorists to metry in the cuprates was extremely surprising because, unlike a representative cuprate contains regions of superconductivity, dopings. Even though it was known before the discovery of high- explore new explanations for s-wave pairs, d-wave Cooper pairs can potentially be broken regions of magnetic order, and a region (called the pseudogap) temperature superconductors that antiferromagnetically mediated s the superconducting state. by impurities. where Tc decreases but the system’s behaviour above Tc is qualita- interaction is attractive in the d-wave channel, it took time to

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CCSep17_HTSTHEORY.indd 44 02/08/2017 16:09 CCSep17_HTSTHEORY.indd 45 02/08/2017 16:09 CERNCOURIER www. V o l u m e 5 7 N u m b e r 7 S e p t e m b e r 2 0 1 7 CERN Courier September 2017 CERN Courier September 2017 HTS theory HTS theory B Glowacki October 1993 pʹ HgBa2Ca2CU3O8-x March 1988 Woodstock physics Ti2Ba2Ca2Cu3O10-x (K)

pair formation and locking of the phases of the pairs occur simulta- In 1986, however, Bednorz and Müller made the breakthrough dis- CeCu2Si2 discovered in 1979 by Steglich, and an organic supercon-

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mental results show that the pseudogap phase in hole-doped cuprates may actually be a state with a broken symmetry, or at CERN puts high-temperature superconductors to use least becomes unstable to such a state at a lower temperature. Evi- strange metal dence has been reported for the breaking of time-reversal, inver- A few years ago, triggered by conceptual studies for a post-LHC collider, Inna Vishik, UCDavis sion and lattice rotational symmetry. Improved instrumentation CERN launched a collaboration to explore the use of high-temperature TN in recent years also led to the discovery of a charge-density wave superconductors (HTS) for accelerator magnets. In 2013 CERN partnered * T and pair-density wave order in the phase diagram and perhaps with a European particle accelerator R&D project called EuCARD-2 to even loop-current order. Many of us believe that the additional develop a HTS insert for a 20 T magnet. The project came to an end in April pseudogap orders observed in the pseudogap phase are relevant to the under- this year, with CERN having built an HTS demonstration magnet based on standing of the full phase diagram, but that these do not change an “aligned-block” concept for which coil-winding and quench-detection T CDW the two key pillars of our understanding: superconductivity is technology had to be developed. Called Feather2, the magnet has a field of 3 T

temperature mediated by short-range magnetic excitations, and the reduction based on low-performance REBCO (rare-earth barium-copper-oxide) tape. of T at smaller dopings is due the existence of a Mott insulator The next magnet, based on high-performance REBCO tape, will approach a charge order c near zero doping. stand-alone field of 8 T. Then, once it is placed inside the aperture of the 13 T “Fresca2” magnet, the field should go beyond 20 T. Why cuprates still matter Now the collaborative European spirit of EuCARD-2 lives on in the antiferromagnetic insulator Tc Fermi liquid The cuprates have motivated incredible advances in instrumentation ARIES project (Accelerator Research and Innovation for European Science and experimental techniques, with 1000-fold increases in accuracy and Society), which kicked off at CERN in May. ARIES brings together superconductivity in many cases. On the theoretical side, they have also led to the devel- 41 participants from 18 European countries, including seven industrial opment of new methods to deal with strong interactions – dynamical partners, to help bring down the cost of the conductor, and is co-funded via a contribution of 10 million from the European Commission. 0.0 0.1 0.2 0.3 mean-field theory and various metallic quantum-critical theories are € hole doping, p examples. These experimental and theoretical methods have found In addition, CERN is developing HTS-based transfer lines to feed the new their way into the study of other materials and are adding new chap- superconducting magnets of the High Luminosity LHC based on magnesium Fig. 4. The phase diagram of a typical cuprate superconductor. ters to standard solid-state physics books. Some of them may even diboride (MgB2), which can be operated in helium gas at temperatures of up to When plotted as a function of temperature and hole-doping, p one day find their way into other fields, such as strongly interacting around 30 K and must be flexible enough to allow the power converters to be (where p = 0 means one conduction electron per copper atom), quark–gluon matter. We can now theoretically understand a host of installed hundreds of metres away from the accelerator. The relatively low cost many different phases appear: the most prominent are the phenomena in high-temperature superconductors, but there are of MgB2 led CERN’s Amalia Ballarino to enter a collaboration with industry, antiferromagnetism near p = 0 and a superconductivity dome at still some important points to clarify, such as the mysterious linear which resulted in a method to produce MgB2 in wire form for the first time. The larger doping. In the “pseudogap” region, states disappear at temperature dependence of the resistivity. team has since achieved record currents that reached 20 kA at a temperature low energy, while above this line the metallic state is different The community is coming together to solve these remaining above 20 K, thereby proving that MgB2 technology is a viable solution for from an ordinary metal and is called a strange metal. issues. Yet, the cynical view of the cuprate problem is that it lacks an long-distance power transmission. The new superconducting lines could also obvious small parameter, and hence a universally accepted theory find applications in the Future Circular Collider initiative. The Feather2 HTS demonstration magnet pictured in CERN’s develop various computational approaches, and today the computed – the analogue of BCS – will never be developed. While it is true ● Matthew Chalmers, CERN. SM18 facility in July.

value of Tc is in the range consistent with experiments. At smaller that serendipity will always have its place in science, we believe dopings, a more reliable approach is to start from a Mott insulator. that the key criterion for “the theory” of the cuprates should not be a This approach also gives d-wave superconductivity, with the value perfect quantitative agreement with experiments (even though this it still makes sense to look at the internal dynamics of a Cooper pair A-M Tremblay 2013 “Strongly correlated superconductivity” in Emergent Phenomena in Correlated Matter Modeling and Simulation, Vol. 3 Verlag des of Tc most likely determined by phase fluctuations and decreasing is still a desirable objective). Rather, a theory of cuprates should be to check whether one can detect traces of spin, charge or even orbital as a function of decreased doping. Because both approaches give judged by its ability to explain both superconductivity and a host fluctuations. At the same time, perturbation theory in the usual sense Forschungszentrum Jülich. F Wilczek 2000 Nucl. Phys. A 257. d-wave superconductivity with comparable values of Tc, the majority of concomitant phenomena, such as the pseudogap, and its ability does not work. Instead, we have to rely more heavily on large-scale 663 of researchers believe that the mechanism of superconductivity in to provide design principles for new superconductors. Indeed, this computer calculations, variational approaches and effective theo- the cuprates is understood, at least qualitatively. is precisely the approach that allowed the recent discovery of the ries. The question of what “binds” fermions into a Cooper pair still Résumé

A more subtle issue is how to explain the so-called pseudogap highest-Tc superconductor to date: hydrogen sulphide. At present, makes sense in this new paradigm, but the answer is often more Dompter la supraconductivité à haute température phase in hole-doped cuprates (figure 4). Here, the system is nei- powerful algorithms and supercomputers allow us to predict quite nuanced than in a weak coupling limit. ther magnetic nor superconducting, yet it displays properties that accurately the properties of materials before they are synthesised. Many challenges are left in the HTS field, but progress is rapid Il y a 30 ans, Johannes Bednorz et Karl Müller recevaient le prix clearly distinguish it from a normal, even strongly correlated For strongly correlated materials such as the cuprates, these calcu- and there is much more consensus now than there was even a few Nobel de physique pour la découverte de matériaux céramiques metal. One natural idea, pioneered by Philip Anderson, is that lations profit from physical insight and vice versa. years ago. Finally, after 30 years, it seems we are closing in on a devenant supraconducteurs à des températures relativement élevées. the pseudogap phase is a precursor to a Mott insulator that con- From a broader perspective, studies of HTS have led to renewed theoretical understanding of this both useful and fascinating mac- D’autres types de supraconducteurs à haute température, présentant tains a soup of local singlet pairs of fermions: superconductivity thinking about perturbative and non-perturbative approaches to roscopic quantum state. des températures de transition encore plus élevées, ont depuis été arises if the phases of all singlet pairs are ordered, whereas anti- physics. Physicists like to understand particles or waves and how découverts, laissant entrevoir des perspectives attrayantes pour des ferromagnetism arises if the system develops a mixture of spin they interact with each other, like we do in classical mechanics, and ● Further reading applications à température ambiante. Le mécanisme gouvernant singlets and spin triplets. Several theoretical approaches, most perturbation theory is the tool that takes us there – QED is a great PW Anderson 1963 Phys. Rev. 130 439. la supraconductivité à haute température s’est révélé difficile à notably dynamical mean-field theory, have been developed to example that works because the fine-structure constant is small. In PW Anderson 1987 Science 235 1196. comprendre, mais les théoriciens approchent à présent d’une théorie quantitatively describe the precursors to a Mott insulator. a single-band solid where interactions are not too strong, it is natural J Bardeen et al. 1957 Phys. Rev. 108 1175. pratique de cet état quantique macroscopique. The understanding of the pseudogap as the phase where elec- to think of superconductivity as being mediated by, for example, the D M Basov and A Chubukov 2011 Nature Physics 7 272 tron states progressively get localised, leading to a reduction of exchange of antiferromagnetic spin fluctuations. When interactions J Bednorz and K Mueller 1986 Zeitschrift für Physik B 64 189. André-Marie Tremblay, Institut quantique, Université de Sherbrooke, and A Drozdov et al. 2015 Nature 73. Tc, is accepted by many in the HTS community. Yet, new experi- are so strong that the wave functions become extremely entangled, 525 Andrey Chubukov, University of Minnesota, Minneapolis.

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A w A r d s IOP awards for 2017 announced

Each year, the UKʼs Institute of Physics (IOP) has won the James Chadwick Medal and recognises outstanding and exceptional Prize, for his “outstanding contributions contributions to physics. 2017 sees five awards to the experimental study of heavy quarks go to those working in high-energy physics. and CP violation, most especially for his David Charlton of the University of leadership of, and his decisive contributions Birmingham in the UK received the Richard to, the LHCb experiment”. Nigel Glover of Glazebrook Medal and Prize (an IOP gold Durham University also won a subject medal medal) for his leadership in experimental – the John William Strutt, Lord Rayleigh Register Interest at www.icec27-icmc2018.org work on the electroweak standard model, Medal and Prize – for pioneering new beginning with the study of Z-boson decays methods for the application of perturbative at LEP and culminating in the discovery quantum chromodynamics to high-energy of the Higgs boson at the LHC. He worked processes involving energetic jets, leading to on OPAL from 1989 to the end of data sophisticated simulation codes that are being taking at LEP, and on ATLAS where he was used to describe LHC data. spokesperson from 2013–2017. Fellow gold Finally, the Clifford Patterson Medal and Register Now! medalist, winning the Dirac medal and Prize, Prize, awarded for exceptional early career Conference 14-18 September 2017 is Michael Duff of Imperial College London contributions to the application of physics Exhibition 15-19 September 2017 and Oxford University, for his “sustained in an industrial or commercial context, groundbreaking contributions to theoretical went to Ceri Brenner of the UK Science and physics including the discovery of Weyl Technology Facilities Council, for “driving anomalies, for having pioneered Kaluza– the development of laser-driven accelerators Klein supergravity, and for recognising for applications and for leading collaborative that superstrings in 10 dimensions are partnerships between academia and industry Researchers working in high-energy physics merely a special case of membranes in an vital for the transfer of this technology were awarded five prizes from the UK 11-dimensional M-theory”. to tackle global challenges”. The awards Institute of Physics (clockwise from top left): Former LHCb spokesperson, Guy will be presented at a ceremony in London David Charlton, Michael Duff, Guy Wilkinson of the University of Oxford, in November. Wilkinson, Nigel Glover and Ceri Brenner. Flerov prize for Witold Nazarewicz. nuclides, and his calculations have helped IBC2017 superheavy elements to clarify the unusual properties of these elements. The World’s Leading Media, Entertainment & A special Flerov prize for experimental Technology Show The 2017 Joint Institute for Nuclear research of heavy nuclei and synthesis Research (JINR) Flerov Prize has of elements with atomic numbers 115 Join over 1,700 exhibitors showcasing the latest technological been awarded to Witold Nazarewicz of (moscovium) and 117 (tennessine) was also innovations, 400+ speakers delivering the latest industry Michigan State University in the US awarded to James Roberto of Oak Ridge insights and 55,000+ attendees providing unlimited networking opportunities at IBC’s 50th annual conference and exhibition. for his contribution to the theoretical National Laboratory, Alexander Shushkin understanding of the properties of the (Elektrokhimpribor, Russia) and Vladimir heaviest elements. Nazarewicz’s research Utyonkov (JINR, Dubna). Over the last two Register at show.ibc.org focuses on rare isotopes, including decades, collaboration between JINR and #IBCShow superheavy nuclei and the heaviest elements US labs has changed our understanding of

that lie at the current borders of the chart of JINR the upper regions of the period table.

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