Superinsulators: The Hideout of Magnetic Monopoles

Dr Maria Cristina Diamantini Dr Carlo A. Trugenberger Professor Valerii M. Vinokur SUPERINSULATORS: THE HIDEOUT OF MAGNETIC MONOPOLES

Magnetic monopoles have long been dismissed as impossible by many physicists, but their existence has nonetheless been theorised for many decades. Through their extensive research, scientists at Terra Quantum AG, the University of Perugia, and SwissScientific Technologies, show that the end could soon be in sight for this conflict. The team’s investigations into superconducting materials not only show that magnetic monopoles must be real – their discoveries also set the stage for exciting technological advances.

Single or Matched? However, this situation didn’t last. In the 1930s, Paul Dirac expressed doubt The concept of single electrical charge is in the idea of a fundamental difference ubiquitous in physics. Whether they are between the properties of electrical and protons, , or , particles magnetic charges, whose resulting fields carrying either positive or negative are otherwise treated in similar ways in charges are crucial to understanding Maxwell’s equations. Through ground- many fundamental aspects of our breaking theoretical calculations, he universe. showed for the first time how magnetic monopoles could exist after all. Meanwhile, however, magnetism appears to operate under a different Dirac’s Case for Monopoles set of rules. Instead of being single, magnetic charges come in inseparable Dirac’s ideas did not appear intuitive at pairs – like the north and south poles first, but lead to a perfectly consistent in a bar magnet – which are connected quantum theory of electromagnetism, Maxwell’s equations. Furthermore, if by looping field lines. If such a magnet including both electric and magnetic combined with other fundamental were broken in half, their two poles charges. Magnetic charges cannot exist, forces – namely the strong and would not simply separate. Instead, they because they lead to unacceptable weak nuclear interactions – a theory would each re-form an opposing pole – singularities. However, if the product emerges for the formation of magnetic creating two new bar magnets. of the magnetic and electric charges monopoles shortly after the Big Bang, is an integer multiplied by ‘the when temperatures across the universe This principle is at the centre of the Planck constant’, these singularities were vastly hotter than they are today. theory that isolated magnetic charges, become unobservable. The Planck named ‘magnetic monopoles’, cannot constant is an important value in Despite the robust reasoning and possibly exist. The idea was even physics demonstrating that quantum elegant outcomes of Dirac’s theory, expressed in the foundational equations mechanics underlies our world. researchers have still found no of electromagnetism, first set out by experimental evidence for such James Clerk Maxwell in the 1860s – and Crucially, Dirac’s idea removes the fundamental magnetic monopoles stood unopposed for many decades inexplicable asymmetry between the to date, even after many decades of afterwards. properties of both charges within searching. So far, several studies have

WWW.SCIENTIA.GLOBAL offered tantalising glimpses of the pair’ of electrons, which can flow switch around entirely, and a Josephson effects predicted by his ideas, but hard through the material without dissipating junction array can fall into a new state, evidence for them still remains elusive. any of their energy in the form of heat. which they called a ‘superinsulator’. At ultra-low temperature, they Now, through extensive research, is a key example of a predicted that these materials have Dr Maria Cristina Diamantini at quantum effect that can be observed on an infinite electrical resistance, the University of Perugia, Dr Valerii macroscopic scales. It contrasts with the making it impossible for Cooper pairs Vinokur at Terra Quantum, and Dr common misconception that quantum to flow through them. As a result, Carlo Trugenberger at SwissScientific laws can only apply to small groups of superinsulators are ‘twin mirror images’ Technologies, predict that this long- particles, or over minuscule distances. of superconductors in terms of their standing deadlock could soon be The effect has now been known and physical properties. about to change, by pointing out studied for well over a century, but that magnetic monopoles should several of its aspects remain a mystery In their study, Dr Diamantini, Dr be searched for in materials in the to physicists. Superconductors can be Trugenberger and a colleague laboratory rather than in the cosmos. homogenous materials or synthetic demonstrated that superinsulating arrangements of superconducting states could emerge close to the point Advances in Superconductivity granules, called ‘Josephson junction of transition between superconducting arrays’. In Josephson junction arrays, and insulating states within Josephson The team’s theories originate from Cooper pairs exhibit quantum tunnelling junction arrays. Further to the insulating an effect that appears at first to be between adjacent superconducting side, Cooper pairs would less readily unconnected to the search for magnetic granules, mediating an electric current tunnel between different granules, but monopoles. First discovered as far with no energy loss. would not be stopped entirely. At just back as 1911, superconductivity is a the right point, however, they predicted phenomenon that allows electrical Superinsulators: The Hidden Face of that the material’s conductivity would currents to flow through some materials Superconductors drop straight to zero. with zero resistance. It arises in certain materials at ultra-cold temperatures, In 1996, theoretical studies of regular Such an idea implied the need for where pairs of oppositely-spinning Josephson junction arrays led Dr a duality between the properties electrons couple together through the Diamantini and Dr Trugenberger to a of electrical and magnetic charges: effect of exchange by lattice vibrations new discovery: under certain conditions, a principle that itself relied on the called ‘phonons’. The result is a ‘Cooper the superconducting properties can existence of magnetic monopoles. The

WWW.SCIENTIA.GLOBAL team’s discovery was so unexpected at first that it didn’t receive much attention following its initial discovery. As a result, their findings remained largely unvisited for over a decade.

Rediscovery and New Understanding

In 2008, exploring superconductor-insulator transitions in a seemingly unrelated physical system, strongly disordered thin films, Dr Vinokur and his research team discovered that upon cooling, the conductivity of an insulating film suddenly drops to zero at a certain temperature – decreasing its magnitude over a million times. This drop is the opposite to superconducting behaviour: when taken across the superconductor-insulator transition onto the superconducting side, the same film displayed a drop to zero electric resistance at superconducting transition temperature. Having followed in Kamerlingh Onnes footprints, Dr Vinokur’s team also independently termed this newly discovered state with zero conductivity a ‘superinsulator’. Dr Vinokur and his colleagues conjectured that close to the Characteristics of Quantum Fluids superconductor-insulator transition, the films self-organise into arrays of superconducting droplets coupled by Josephson Using the Heisenberg uncertainty principle brought about tunnelling. Indeed, they demonstrated that near this transition, an understanding that is now supported by experiments, these disordered films behave exactly as regular Josephson whereby the effect of infinite resistance at finite temperatures junction arrays, as if there was no disorder whatsoever. observed by Dr Vinokur’s team at the insulating side of the superconductor-insulator transition stems from formation of Dr Vinokur’s team has built a solid understanding of the origin the Bose condensate of magnetic charges. of a superinsulator on the foundational concept of quantum mechanics: the Heisenberg uncertainty principle. This principle This Bose condensate is a mirror twin of the Bose states that it is impossible to measure two conjugated variables condensate of paired electrons that is characteristic for the of a quantum system (for example, the position and the superconducting state. Therefore, duality between electrical momentum of a particle) with absolute precision. The more and magnetic charges emerged again – now as a consequence accurately we know one of these variables, the less accurately of the most fundamental concept of quantum mechanics – and we can measure the other. was strongly evidenced by experiment.

Josephson junction arrays host two conjugated entities: Squeezed Magnetic Filaments Cooper pairs, representing electric charges, and superconducting vortices that impersonate magnetic charges. The second fundamental effect characteristic to In superconductors, Cooper pairs form quantum fluid called superconductivity to stem from Bose condensates of a ‘Bose condensate’ that manifests quantum properties on paired electrons emerges when superconductors are macroscopic scales. penetrated by magnetic fields. According to Maxwell’s laws of electromagnetism and the hydrodynamics of charged The basic experimental fact about superconductors is that the superfluid liquids, this causes superfluid paired electrical number of ‘magnetic charges’ is always known and fixed. This charges within a material to move in circular paths around the means that the number of Cooper pairs in the Bose condensate magnetic field lines. is fully uncertain and they move without scattering (otherwise one could have counted them), and hence, without resistance. In turn, the magnetic fields created by these circularly moving charges will squeeze the external magnetic field lines into By reversing the uncertainty principle, Dr Vinokur and his extremely thin filaments. These circling currents are known colleagues ruled that fixing electric charges implies that as ‘Abrikosov vortices’, and are a key demonstration that magnetic vortices arbitrarily fluctuate around and become homogeneous superconductivity and homogeneous magnetic indistinguishable, forming a Bose condensate of magnetic fields cannot coexist. Superconductors that allow for the charges. According to fundamental law of superconductivity, penetration of a magnetic field in the form of Abrikosov vortices the ‘Josephson effect’, moving vortices create finite voltage. are called ‘type II superconductors’. And finite voltage in the absence of current implies infinite resistance, hence formation of a superinsulator. Josephson junction arrays host a slightly different kind of magnetic vortices, which can exercise quantum tunnelling in

WWW.SCIENTIA.GLOBAL the grainy Josephson junction arrays paths around any electric fields that be studied indirectly through high- observed in Dr Vinokur’s experiments. penetrate the material. In the same way energy collisions, and are still poorly This behaviour mirrors the Cooper pairs’ that superconductors expel magnetic understood. Such a property is notably tunnelling between superconducting fields, this process squeezes electric comparable with the impossibility of granules and supports the picture fields into thin filaments, which tightly separating the magnetic charges in of duality between the properties bind positive and negative charges a bar magnet – and according to the of electrical and magnetic charges. together. In turn, any free flow of current researchers, this is no coincidence. According to Drs Diamantini and is completely eliminated, resulting in an Trugenberger’s earlier theories, perfectly infinite resistance in the material. Previous studies have given rise to mirrored processes should also play theories involving a property named out on the superinsulating side of the Clearly, this behaviour perfectly mirrors ‘colour’. They suggest that quarks transition – demanding the presence of that of the magnetic filaments that interact via the strong force by magnetic monopoles. form on the other side of the transition exchanging three possible colours – fully realising the duality between – whose exact physical nature is Until then, such effects had gone almost electrical and magnetic charges first still far from clear. In their research, entirely unexplored – but this was put forward by Dirac. In addition, the Dr Diamantini, Dr Vinokur and Dr about to change through the combined electric filaments display a remarkable Trugenberger noted remarkably similar research of Dr Vinokur, Dr Diamantini, Dr similarity with – bound states of roles in the electric filaments observed Trugenberger, and their colleagues. quarks. These fundamental particles in their superinsulators. are described by the Standard Model of Parallels in Superinsulators particle physics, and form the basis of In particular, the Cooper pairs bound by : a family of particles including the filaments have the same electrical After more than a decade of repeating protons, neutrons, pions and a diverse properties of particles named ‘pions’: and improving on this initial experiment, range of other, more exotic particles. hadrons containing one of either an up the team has now gathered indisputable or a down , and one of either of proof of this effect. Through their -like Strings their antimatter counterparts. Moreover, observations, they have discovered this behaviour can be modelled using a necessity for magnetic monopoles Because of the strong nuclear force, a just one colour – avoiding the need to to exist on the superinsulating side of quark can never be observed outside make any assumptions about unknown Josephson junction array transitions. of a . If a physicist ever attempts aspects of fundamental physics. Such to isolate a quark, other quarks will be a clear analogy could soon shed new Moreover, these singular charges must generated spontaneously to ensure light on a difficult problem in particle behave just like quantum particles – the laws of physics are not broken. As a physics. forming Bose condensates at ultra-low result, the mechanisms used by quarks temperatures, which flow in circular to bind together into hadrons can only

WWW.SCIENTIA.GLOBAL Generalising the Picture temperature superconductors, where pairing mechanisms would need to be far stronger. Up until this point, Drs Vinokur, Diamantini, and Trugenberger had only studied the properties of superconductor-insulator Instead, the researchers have suggested an entirely different transitions in 2D. To gain a full picture of the physics involved, route to formation, based on the attraction they would need to extend their predictions to a more provided by magnetic monopoles. Unlike phonons, monopole- generalised, 3D case. From their earlier descriptions of electric based mechanisms would allow electrons to become paired filament confinement as a mechanism for superinsulation, even when higher temperatures introduce more vibrations alongside previous theories of the quantum fields that underly to atomic lattices – which would otherwise drown out the the universe’s fundamental particles, the team has now made information carried by individual phonons. this step in their latest research. This insight could soon be exploited by engineers to design Through these studies, they have found that magnetic new materials specially tailored to display superconductivity at monopoles can display even more exotic behaviours in 3D room temperatures: now one of the most widely pursued goals materials. In particular, they discovered clear evidence for in materials physics. electrical charges being carried on top of magnetic monopoles: particles named ‘dyons’ by theoretical physicists. Furthermore, Unifying Two Charges these particles can also settle into Bose condensates when cooled, giving rise to even further intriguing properties. For nearly a century since Dirac’s initial theories, the very idea of a symmetry between singular magnetic and electrical charges These observations have now improved physicists’ has been either heavily doubted, or dismissed entirely by many understanding of the once mysterious effect of high- physicists. Yet through their ground-breaking discoveries of the temperature superconductivity, which enables current to crucial roles played by magnetic monopoles in providing a full flow with zero resistance at above ultra-cold temperatures. picture of the duality of superconducting materials, Drs Vinokur, The researchers have now clearly shown that this behaviour Diamantini, and Trugenberger are rapidly transforming this can arise from the interplay between Cooper pairs and dyon picture. condensates – once again, showcasing the key role of magnetic monopoles. Not only do the team’s ideas hold the potential to unify the physics of magnetic charges with those of electrical charges A New Mechanism for Attraction – the technological implications would also be profound. Through new ways to produce high-temperature and even Through this improved understanding, Drs Diamantini, room-temperature superconductors, researchers could Trugenberger and Vinokur were next able to shed new light soon produce technologies ranging from extremely high- on the mechanism that allows electrons to become paired in performance sensors, to electrical circuits in which no energy the first place, through interactions within their host materials. is lost to heat. In turn, such discoveries could pave the way to Previously, this mechanism was thought to be particle-like tackling some of the newest and most exciting technological vibrations named ‘phonons’, which travel through solid challenges emerging today. atomic lattices. However, this would no longer work in high-

WWW.SCIENTIA.GLOBAL Meet the researchers Dr Maria Cristina Diamantini Dr Carlo A. Trugenberger Professor Valerii M. Vinokur University of Perugia SwissScientific Technologies SA Terra Quantum AG Perugia Geneva Rorschach Italy Switzerland Switzerland

Dr Maria Cristina Diamantini completed Dr Carlo Trugenberger obtained his PhD Professor Dr Valerii Vinokur completed her PhD in theoretical physics at the in theoretical physics at ETH Zurich in his PhD in theoretical condensed matter University of Perugia in 1995. She then 1988, and then pursued an international physics at the Institute for Solid State held positions at both CERN and the academic career, eventually becoming Physics of the Academy of Sciences University of Oxford with a fellowship of an associate professor of physics at of USSR in Chernogolovka in 1979, the Swiss National Science Foundation, the University of Geneva. He then went where he worked until 1990. In 1990, he while becoming a Humboldt fellow on to found two artificial intelligence assumed an appointment at Argonne at the Free University in Berlin. She companies – one of which he continues National Laboratory, USA. In 2021, now teaches Theoretical Physics and to manage today. Dr Trugenberger’s he retired from his position of Senior Statistical Mechanics at the University research interests lie in both theoretical Scientist and Argonne Distinguished of Perugia, and is part of the Noise condensed matter physics and Fellow, to join Terra Quantum AG as in Physical Systems Laboratory in quantum gravity, and he continues its Chief Technology Officer in the US. Perugia and of Italy’s National Institute to be an active part of both research Professor Vinokur is a Foreign Member for Nuclear Physics (INFN, Perugia’s communities. of the National Norwegian Academy section). Dr Diamantini has now of Science and Letters and Fellow of been part of a wide variety of exciting CONTACT the American Physical Society. He research projects across Europe. has won numerous awards for his E: [email protected] groundbreaking research, including CONTACT W: https://www.swissscientific.com/ the International John Bardeen Prize about in 2003, the Alexander von Humboldt E: [email protected] Research Award in both 2003 and 2013, W: https://www.unipg.it/personale/ and the Fritz London Memorial Prize in maria.diamantini/didattica 2020.

CONTACT

E: [email protected] W: https://terraquantum.swiss/team/ prof-dr-valerii-vinokur/

KEY COLLABORATORS

Professors Tatyana Baturina and Alexey Mironov, Novosibirsk State University, Russia Professor Christoph Strunk, University of Regensburg, Germany Professor Philip Kim, Harvard University Professor Yakov Kopelevich, Universidade Estadual de Campinas-UNICAMP, Brazil Dr Svetlana Postolova, Institute for Physics of Microstructures RAS, Nizhny Novgorod, Russia Dr Mikhail Fistul, Ruhr University, Bochum, Germany Professor Luca Gammaitoni, University of Perugia, Italy

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