1.0. Introduction:

Cryogenics is the field of physics dedicated to the study of extremely low temperatures. By the beginning of the 20th century, this had become a very popular area of research, with many scientists, including the likes of Caillete and Pictet (who first liquified air in 1877), racing to achieve temperatures closer and closer to absolute zero. In early 1908, Heike Onnes, a Dutch physicist, achieved the first ever liquefaction of helium, using a technique based on the Joule-Kelvin principle that involved forcing helium out of a small valve and thus bringing about a rapid decrease in pressure and temperature. In 1911, Onnes decided to use this technique to experiment with the effects of extremely low temperatures on the resistance of electrical conductors, and by April of that same year, he had made a remarkable discovery that would open up an entirely new field of physics.

            As Onnes passed a current through a pure mercury wire, and continually measured its resistance, he steadily lowered the temperature using liquified helium. Contrary to what he had expected, there was no levelling off of the resistance, though even more surprisingly, at a temperature of 4.2°K, the resistance suddenly vanished. (See Figure 1.) The ability of an electrical conductor to have a resistance of zero had traditionally been conceived impossible, and so it is understandable why, in 1913, Onnes was awarded the Nobel Prize in Physics for investigations on the properties of matter at low temperatures as well as the liquefaction of helium. Onnes labelled this new state of zero resistance ‘superconductivity’, and over the next few decades, many other metals were found to exhibit this property as their temperatures were lowered below what is referred to as their ‘critical temperature’ or Tc.

Figure 1: Resistivity against temperature for a non-superconductor and a superconductor

2.0. Superconductors:

2.1. Explaining Superconductivity – the BCS theory:

The importance of Onnes’ discovery was immediately apparent to the scientific community: an electrical conductor with no resistance would be able to carry current any distance and for any amount of time, with no dissipation of energy. However, due to the sheer difficulty of cooling a superconductor below its critical temperature and then keeping it at that temperature, it soon became clear that the introduction of superconductors to large-scale electric power transmission was not at all plausible. In addition, the challenge of keeping a superconductor below its Tc meant that superconductivity was a difficult field to study in the first few decades after its discovery.  In fact, it was almost half a century after Onnes’ discovery that the first widely-accepted microscopic theory of superconductivity emerged. In April 1957, this theory was proposed by three physicists at the University of Illinois, John Bardeen, Leon Cooper and Robert Schrieffer, and became to be known as the BCS theory, after the initials of the three physicists’ last names.

The structure of a metal involves positively-charged ions held together by a sea of electrons. When a potential difference is applied across a section of metal, the electrons are able to move, and this is what makes metals effective conductors. Classical physics describes the resistance of a metal as due to collisions between moving electrons and vibrating metal ions. However, not long after the discovery of superconductors, it became apparent that this classical model could never explain the superconducting state, because electrons in any material always experience some collisions, and as a result, resistivity should never be able to be zero.

The BCS theory introduces ideas from quantum mechanics by describing how two electrons in a superconductor are able to interact with each other in a pair known as a Cooper pair. The result of this pairing is observed as a net attractive force between the two electrons, and the simplified classical explanation of this phenomenon is as follows: as the first electron passes metal ions, it causes a momentary deformation in the lattice structure of the ions via electrostatic attraction. This results in a slight increase in the concentration of positive charge in the region, which attracts the second electron in the direction of the first electron’s movement. (See Figure 2.) The interaction is almost instantaneous, as each electron immediately goes on to form a Cooper pair with another electron and the new pair effectively acts as a new and single particle. The BCS theory is expressed in terms of the advanced ideas of quantum mechanics, but in its essence, it states that electrons in a superconductor travel together coherently and collectively. Today, it still stands as the dominant theory behind superconductivity, and it was the reason for which Bardeen, Cooper and Schrieffer were awarded a joint Nobel Prize in Physics in 1972.

Figure 2: A simplified classical explanation of the BCS theory

2.2. Magnetic Properties of Superconductors – the Meissner effect:

Perhaps even more dramatic than the electrical properties of superconductors are their magnetic properties. In 1933, two German physicists, Walther Meissner and Robert Ochsenfeld, were measuring the magnetic field distribution outside a superconducting sample of lead (Tc = 7.2°K), when they detected that as the sample was cooled below its critical temperature, all interior magnetic fields within the sample were cancelled. (See Figure 3.) After the initial observation, Meissner studied this phenomenon in greater depth and discovered that superconductors are able to stop magnetic fields from penetrating their surface by producing magnetic surface currents that exactly counter the external field. This phenomenon was thus called the Meissner effect. It is worth noting that this effect will only occur if the external magnetic field is smaller than the superconductor’s critical magnetic field, Hc; if the magnetic field becomes too great, it will penetrate the interior of the metal and will cause it to lose its superconductivity. Two years after Meissner’s discovery, two British-German physicists, the London brothers, published a set of equations. These became known as the London equations, and they were extremely successful in explaining the Meissner effect by describing certain aspects such as the penetration depth of magnetic fields at T ≈ Tc.

Figure 3: Meissner effect – magnetic field lines excluded from interior

2.3. Quantum Levitation:

The Meissner effect completely explains a phenomenon known as quantum levitation. If a superconductor is cooled below its critical temperature while in a magnetic field, currents will be induced on the surface of the superconductor which create a counter-magnetic force and as a result, the two materials will repel. Thus, the superconductor can be made to levitate over a series of magnets if their magnetic fields are aligned correctly. In fact, the force holding the superconductor away from the magnet is so strong that a 3mm thick superconducting disk is able to support up to 1000kg on top of it (70,000 times its own weight), without touching the magnet.

2.4. High-Tc superconductors and the applications of superconductors:

Since superconductivity was first discovered in 1911, scientists have been continually searching for materials which exhibit higher and higher critical temperatures, in the hope that one day, they might discover a superconductor with a critical temperature of room temperature. Although at present this is very far from being a reality, scientists have discovered compounds which become superconductors at temperatures as high as 133°K. (See Figure 4.) One of the most significant discoveries was made in 1986, when two physicists, Georg Bednorz and Karl Müller, came across a family of crystalline compounds, famous for displaying high-temperature superconductivity. The particular compound, YBa2Cu3O7, was the first ceramic superconductor to be discovered. In addition, it was the first material ever discovered to become superconducting above the boiling point of liquid nitrogen. This made experiments with superconductivity more accessible to the wider world, because liquid nitrogen is a coolant that is more readily available, more inexpensive, safer and easier to handle than liquid helium. Yttrium barium copper oxide compounds seem to be a promising family of materials from which we may discover even higher temperature superconductors in the future. For their work, Bednorz and Müller received the 1987 Nobel Prize in physics.

As a result of higher and higher temperature superconductors being discovered, superconductors now play important roles in a number of new technologies. The first large scale commercial application of superconductivity was for MRI (magnetic resonance imaging). Although normal electromagnets can be used, superconducting magnets can be made to be emit a much stronger magnetic field. In addition, due to a resistivity of zero, they can achieve a high stability of magnetic field, which is essential for the precision, resolution and speed required for clinical imaging. Furthermore, magnetically levitated trains, which employ superconducting electromagnets, are able to float above their tracks. Although it is very expensive not only to construct such trains, but also to keep the superconductors cool, this technology allows us to create significantly faster trains than conventional wheeled passenger trains. For example, in Japan, a new section of the magnetic rail network between Tokyo and Nagoya is estimated to cost a hefty $52bn, however the SCMaglev, a magnetically levitated train that will run on the network, has attained top speeds of over 600km/h in test runs.

Figure 4: The discovery of High-Tc superconductors since 1911

3.0. Quantum Locking:

3.1. Observing Quantum Locking:

Despite the many applications of superconductors, the focus of this essay will now shift towards one application in particular: quantum locking. The phenomenon is comparable to quantum levitation with one distinct difference: instead of a superconductor simply being repelled by a magnet, so that it levitates above it, in certain circumstances it can be made to be locked in place at a specific distance from a magnet. One of the hotspots for research into quantum locking is Tel-Aviv University, and Dr Boaz Almog, from this university, demonstrated quantum locking in his TED talk of 2012. He left a cooled superconductor locked at a distance from a magnet and demonstrated that it stayed in place even after the magnet was turned upside down. The superconductor maintained the exact position and angle at which Dr Almog left it.

3.2. Explaining Quantum Locking – Flux Pinning:

To explain quantum locking, it is first necessary to understand that there are in fact two types of superconductors. This discovery won Alexei Abrikosov, a Russian-American physicist, the 2003 Nobel Prize in Physics (which he shared with two other scientists who had both made contributions to the field of superconductors and their quantum effects). Type I superconductors, which include most pure metals such as mercury, lead and aluminium, will keep out any external magnetic field until a critical applied field, Hc, is reached. At this point, the material will completely lose its superconductive properties. Type II superconductors, on the other hand, include most compounds, such as alloy and ceramic superconductors. They will only keep out the magnetic field until a first critical field, Hc1 is reached. Between this value, and the next critical field value, Hc2 (at which point, it loses its superconductive properties), flux pinning occurs. (See figure 5.)

Flux pinning refers to the partial penetration of the magnetic field in the form of flux lines or vortices. These vortices move apart and attempt to arrange themselves into an orderly array known as a fluxon lattice. On a typical type II superconductor disk with a diameter of 76mm, there are approximately 100 billion flux lines penetrating the disk, and this is why the effect of quantum locking is so strong. Depending on the quality of the superconductor, the vortices may either be able to move freely or they may be strongly pinned in place. Most type II, high temperature superconductors have defects (missing or misplaced atoms) in their lattices, and these prevent the vortices from moving, pinning the magnetic field lines, and stopping any motion relative to the magnet. Thus, the pinning effect allows the superconductor to be locked in place. The phenomenon of flux pinning is closely related to the Meissner effect. Indeed, any superconducting disk locked at a distance from a magnet will be able to support objects up to 70,000 times its own weight before it is forced into contact with the magnet. However, while the Meissner effect simply causes repulsion by shielding the superconductor from all magnetic fields, flux pinning stops flux lines, and thus also the superconductor, from moving in any direction.

Figure 5: Strength of force between superconductor and magnet plotted against applied field

3.3. The Future of Quantum Locking:

While quantum locking does indeed have the potential to amaze a public audience, one of the main reasons as to why it is so exciting is that it holds many real-world applications. Quantum locking will be sure to revolutionise technologies such as lifts, because it allows two objects to be kept at a constant distance away from each other. This could be used for keeping a lift away from the lift shaft walls so it could levitate inside the lift shaft. In addition, if a radial magnet is used with a superconductor, it is able to rotate around its centre, while maintaining its angle to and distance from the magnet. This is likely to prove useful for any rotating surfaces in machinery in the future. The thinner the superconducting layer, the stronger the pinning effect, and this means that there is great potential for the development of completely frictionless joints. Furthermore, quantum locking is likely to completely change transport in the decades to come. For example, a new technology, MagSurf, has already developed by the University of Paris. It uses quantum locking to create a hoverboard effect that can transport a person.

Over the last century, since Onnes’ discovery of superconductivity, superconductors and their quantum effects have been an ever-growing field, from which 4 Nobel Prizes in Physics have emerged. Until fairly recently, most research has gone into explaining these phenomena, however, this is changing. New applications of superconductors and the effects of quantum locking are emerging at an ever-growing rate. Looking forward, quantum locking certainly holds the potential for the discovery of exciting new technologies, from entirely new methods of transportation, to machines that last much longer due to frictionless joints. Without a doubt, superconductors and quantum locking will shape the future of humanity in more ways than we can currently imagine.


Sources:

Bradu, Benjamin. January 2017. “Heike Kamerlingh Onnes: The Liquefaction of Gases.” Accessed February 2020. http://www.bibnum.education.fr/sites/default/files/19-onnes-analysis.pdf.

The Nobel Prize. Last Edited 2020. The Nobel Prize in Physics 1913. Accessed February 2020.

Wikipedia. Last Edited 2019. Cooper pair. Accessed Ferbruary 2020. https://en.wikipedia.org/wiki/Cooper_pair.

Yom, Aria. 2018. “The London Equations.” Physics Courses – The London Equations. Accessed February 2020.

Quantum Experience. n.d. “Quantum Levitation For Undergraduate and High School Teachers.” Quantum Levitation. Accessed February 2020. https://www.quantumlevitation.com/.

Wikipedia. Last Edited February 2020. Yttrium Barium Copper Oxide. Accessed February 2020.

Japan Rail Pass. 2019. The Japanese Maglev: World’s fastest bullet train. June 10. Accessed February 2020.

TED. 2012. The Levitating Superconductor. Accessed February 2020. https://www.ted.com/talks/boaz_almog_the_levitating_superconductor?language=en. 

Orthacker, Angelina. n.d. “Superconductivity.” Accessed February 2020.

Quantum Experience. n.d. “Quantum Levitation For Undergraduate and High School Teachers.” Quantum Levitation. Accessed February 2020. https://www.quantumlevitation.com/

Wikipedia. Last Edited January 2018. Flux pinning. Accessed February 2020. https://en.wikipedia.org/wiki/Flux_pinning.

Bobroff, Julien. 2013. MagSurf: Quantum Physics for Everyone. September. Accessed February 2020.

https://en.wikipedia.org/wiki/Yttrium_barium_copper_oxide.
https://www.nobelprize.org/prizes/physics/1913/summary/.

About the author