Getting started on superconductivity

After the hoopla surrounding and attention on particle physics subsided, I realized that I’d been riding a speeding wagon all the time. All I’d done is used the lead-up to (the search for the Higgs boson) and the climax itself to teach myself something. Now, it’s left me really excited! Learning about particle physics, I’ve come to understand, is not a single-track course: all the way from making theoretical predictions to having them experimentally verified, particle physics is an amalgamation of far-reaching advancements in a host of other subjects.

One such is superconductivity. Philosophically, it’s a state of existence so far removed from its naturally occurring one that it’s a veritable “freak”. It is common knowledge that everything that’s naturally occurring is equipped to resist change that energizes, to return whenever possible to a state of lower energy. Symmetry and surface tension are great examples of this tendency. Superconductivity, on the other hand, is the desistence of a system to resist the passage of an electric current through it. As a phenomenon that as yet doesn’t manifest in naturally occurring substances, I can’t really opine on its phenomenological “naturalness”.

In particle physics, superconductivity plays a significant role in building powerful particle accelerators. In the presence of a magnetic field, a charged particle moves in a curved trajectory through it because of the Lorentz force acting on it; this fact is used to guide the protons in the Large Hadron Collider (LHC) at CERN through a ring 27 km long. Because moving in a curved path involves acceleration, each “swing” around the ring happens faster than the last, eventually resulting in the particle traveling at close to the speed of light.

[caption id="attachment_23890" align="aligncenter" width="627"] A set of superconducting quadrupole-electromagnets installed at the LHC with the cryogenic cooling system visible in the background[/caption]

In order to generate these extremely powerful magnetic fields – powerful because of the minuteness of each charge and the velocity required to be achieved – superconducting magnets are used that generate fields of the order of 20 T (to compare: the earth’s magnetic field is 25-60 μT, or close to 500,000-times weaker)! Furthermore, the direction of the magnetic field is also switched accordingly to achieve circular motion, to keep the particle from being swung off into the inner wall of the collider at any point!

To understand the role the phenomenon of superconductivity plays in building these magnets, let’s understand how electromagnets work. In a standard iron-core electromagnet, insulated wire is wound around an iron cylinder, and when a current is passed through the wire, a magnetic field is generated around the cross-section of the wire. Because of the coiling, though, the centre of the magnetic field passes through the axis of the cylinder, whose magnetic permeability magnifies the field by a factor of thousands, itself becoming magnetic.



When the current is turned off, the magnetic field instantaneously disappears. When the number of coils is increased, the strength of the magnetic field increases. When the strength of the current is increased, the strength of the magnetic field increases. However, beyond a point, the heat dissipated due to the wire’s electric resistance reduces the amount of current flowing through it, consequently resulting in a weakening of the core’s magnetic field over time.

It is Ohm’s law that establishes proportionality between voltage (V) and electric current (I), calling the proportionality-constant the material’s electrical resistance: R = V/I. To overcome heating due to resistance, resistance itself must be brought down to zero. According to Ohm’s law, this can be done either by passing a ridiculously large current through the wire or bringing the voltage across its ends down to zero. However, performing either of these changes on conventional conductors is impossible: how does one quickly pass a large volume of water through any pipe across which the pressure difference is miniscule?!

[caption id="attachment_23893" align="alignright" width="116"] Heike Kamerlingh Onnes[/caption]

The solution to this unique problem, therefore, lay in a new class of materials that humankind had to prepare, a class of materials that could “instigate” an alternate form of electrical conduction such that an electrical current could pass through it in the absence of a voltage difference. In other words, the material should be able to carry large amounts of current without offering up any resistance to it. This class of materials came to be known as superconductors – after Heike Kamerlingh Onnes discovered the phenomenon in 1911.

In a conducting material, the electrons that essentially effect the flow of electric current could be thought of as a charged fluid flowing through and around an ionic 3D grid, an arrangement of positively charged nuclei that all together make up the crystal lattice. When a voltage-drop is established, the fluid begins to get excited and moves around, an action called conducting. However, the electrons constantly collide with the ions. The ions, then, absorb some of the energy of the current, start vibrating, and gradually dissipate it as heat. This manifests as the resistance. In a superconductor, however, the fluid exists as a superfluid, and flows such that the electrons never collide into the ions.

In (a classical understanding of) the superfluid state, each electron repels every other electron because of their charge likeness, and attracts the positively charged nuclei. As a result, the nucleus moves very slightly toward the electron, causing an equally slight distortion of the crystal lattice. Because of the newly increased positive-charge density in the vicinity, some more electrons are attracted by the nucleus.



This attraction, which, across the entirety of the lattice, can cause a long-range but weak “draw” of electrons, results in pairs of electrons overcoming their mutual hatred of each other and tending toward one nucleus (or the resultant charge-centre of some nuclei). Effectively, this is a pairing of electrons whose total energy was shown by Leon Cooper in 1956 to be lesser than the energy of the most energetic electron if it had existed unpaired in the material. Subsequently, these pairs came to be called Cooper pairs, and a fluid composed of Cooper pairs, a superfluid (thermodynamically, a superfluid is defined as a fluid that can flow without dissipating any energy).

Although the sea of electrons in the new superconducting class of materials could condense into a superfluid, the fluid itself can’t be expected to flow naturally. Earlier, the application of an electric current imparted enough energy to all the electrons in the metal (via a voltage difference) to move around and to scatter against nuclei to yield resistance. Now, however, upon Cooper-pairing, the superfluid had to be given an environment in which there’d be no vibrating nuclei. And so: enter cryogenics.

[caption id="attachment_23895" align="aligncenter" width="627"] The International Linear Collider - Test Area's (ILCTA) cryogenic refrigerator room[/caption]

The thermal energy of a crystal lattice is given by E = kT, where ‘k’ is Boltzmann’s constant and T, the temperature. Demonstrably, to reduce the kinetic energy of all nuclei in the lattice to zero, the crystal itself had to be cooled to absolute zero (0 kelvin). This could be achieved by cryogenic cooling techniques. For instance, at the LHC, the superconducting magnets are electromagnets wherein the coiled wire is made of a superconducting material. When cooled to a really low temperature using a two-stage heat-exchanger composed of liquid helium jacketed with liquid nitrogen, the wires can carry extremely large amounts of current to generate very intense magnetic fields.

At the same time, however, if the energy of the superfluid itself surpassed the thermal energy of the lattice, then it could flow without the lattice having to be cooled down. Because the thermal energy is different for different crystals at different ambient temperatures, the challenge now lies in identifying materials that could permit superconductivity at temperatures approaching room-temperature. Now that would be (even more) exciting!

Related articles

• Graphene the Ubiquitous (isnerd.wordpress.com)

P.S. A lot of the related topics have not been covered in this post, such as the Meissner effect, electron-phonon interactions, properties of cuprates and lanthanides, and Mott insulators. They will be taken up in the future as they're topics that require in-depth detailing, quite unlike this post which has been constructed as a superfluous introduction only.

Graphene the Ubiquitous

Every once in a while, a (revolutionary-in-hindsight) scientific discovery is made that's at first treated as an anomaly, and then verified. Once established as a credible find, it goes through a period where it is subject to great curiosity and intriguing reality checks - whether it was a one-time thing, if it can actually be reproduced under different circumstances at different locations, if it has properties that can be tracked through different electrical, mechanical and chemical circumstances.

After surviving such tests, the once-discovery then enters a period of dormancy: while researchers look for ways to apply their find's properties to solve real-world problems, science must go on and it does. What starts as a gentle trickle of academic papers soon cascades into a shower, and suddenly, one finds an explosion of interest on the subject against a background of "old" research. Everybody starts to recognize the find's importance and realize its impending ubiquity - inside laboratories as well as outside. Eventually, this accumulating interest and the growing conviction of the possibility of a better, "enhanced" world of engineering drives investment, first private, then public, then more private again.

Enter graphene. Personally, I am very excited by graphene as such because of its extremely simple structure: it's a planar arrangement of carbon atoms a layer thick positioned in a honeycomb lattice. That's it; however, the wonderful capabilities that it has stacked up in the eye of engineers and physicists worldwide since 2004, the year of it's experimental discovery, is mind-blowing. In the fields of electronics, mensuration, superconductivity, biochemistry, and condensed-matter physics, the attention it currently draws is a historic high.

Graphene's star-power, so to speak, lies in its electronic and crystalline quality. More than 70 years ago, the physicist Lev Landau had argued that lower-dimensional crystal lattices, such as that of graphene, are thermodynamically unstable: at some fixed temperature, the distances through which the energetic atoms vibrated would cross the length of the interatomic distance, resulting in the lattice breaking down into islands, a process called "dissolving". Graphene broke this argument by displaying extremely small interatomic distances, which translated as improved electron-sharing to form strong covalent bonds that didn't break even at elevated temperatures.

As Andre Geim and Konstantin Novoselov, experimental discoverers of graphene and joint winners of the 2010 Nobel Prize in physics, wrote in 2007:

The relativistic-like description of electron waves on honeycomb lattices has been known theoretically for many years, never failing to attract attention, and the experimental discovery of graphene now provides a way to probe quantum electrodynamics (QED) phenomena by measuring graphene’s electronic properties.

(On a tabletop for cryin' out loud.)

What's more, because of a tendency to localize electrons faster than could conventional devices, using lasers to activate the photoelectric effect in graphene resulted in electric currents (i.e., moving electrons) forming within picoseconds (photons in the laser pulse knocked out electrons, which then traveled to the nearest location in the lattice where it could settle down, leaving a "hole" in its wake that would pull in the next electron, and so forth). Just because of this, graphene could make for an excellent photodetector, capable of picking up on small "amounts" of eM radiation quickly.



An enhanced current generation rate could also be read as a better electron-transfer rate, with big implications for artificial photosynthesis. The conversion of carbon dioxide to formic acid requires a catalyst that operates in the visible range to provide electrons to an enzyme that its coupled with. The enzyme then reacts with the carbon dioxide to yield the acid. Graphene, a team of South Korean scientists observed in early July, played the role of that catalyst with higher efficiency than its peers in the visible range of the eM spectrum, as well as offering up a higher surface area over which electron-transfer could occur.

Another potential area of application is in the design and development of non-volatile magnetic memories for higher efficiency computers. A computer usually has two kinds of memories: a faster, volatile memory that can store data only when connected to a power source, and a non-volatile memory that stores data even when power to it is switched off. A lot of the power consumed by computers is spent in transferring data between these two memories during operation. This leads to an undesirable difference arising between a computer's optimum efficiency and its operational efficiency. To solve for this, a Singaporean team of scientists hit upon the use of two electrically conducting films separated by an insulating layer to develop a magnetic resistance between them on application of a spin-polarized electric field to them.

The resistance is highest when the direction of the magnetic field is anti-parallel (i.e., pointing in opposite directions) in the two films, and lowest when the field is parallel. This sandwiching arrangement is subsequently divided into cells, with each cell possessing some magnetic resistance in which data is stored. For maximal data storage, the fields would have to be anti-parallel as well as that the films' material spin-polarizability high. Here again, graphene was found to be a suitable material. In fact, in much the same vein, this wonder of an allotrope could also have some role to play in replacing existing tunnel-junctions materials such as aluminium oxide and magnesium oxide because of its lower electrical resistance per unit area, absence of surface defects, prohibition of interdiffusion at interfaces, and uniform thickness.

In essence, graphene doesn't only replace existing materials to enhance a product's (or process's) mechanical and electrical properties, but also brings along an opportunity to redefine what the product can do and what it could evolve into in the future. In this regard, it far surpasses existing results of research in materials engineering: instead of forging swords, scientists working with graphene can now forge the battle itself. This isn't surprising at all considering graphene's properties are most effective for nano-electromechanical applications (there have been talks of a graphene-based room-temperature superconductor). More precise measurements of their values should open up a trove of new fields, and possible hiding locations of similar materials, altogether.

The politico-religious wave

An electromagnetic (em) wave travels through space at an astounding 299,792,458 m/s. This number, colloquially known as the speed of light (a form of em radiation), is the speed limit for anything that moves in the universe. While such a wave moves through space, it barely loses its energy. Light from an exploding star billions of lightyears away reaches Earth, and retains the signature that dignifies it as light from a dying star—even after travelling through space for billions of years. How does it do that? The answer illustrates the ideal symbiotic relationship: an electric field that generates a magnetic field, and a magnetic field that generates an electric field, each perpendicular to the other, each feeding into the other, carrying themselves through space and time.



This description of the propagation of an electromagnetic wave parallels, with striking similarity, the relationship between politics and religion. Each entity thrives on polarization, on creating and consuming potentials, on penetrating all regions of space unless shielded by some leaden obstacle. Even though each is a necessary manifestation of humanism, one is dissociated from all mortality—exhibiting a dangerous tendency to be omnipresent—and the other is associated closely with the very act of being—wielding an omnipotent weapon. Of course, in the course of their independent existence, they are strong, weak, focused, diffuse, directional, pregnant, and many other things. Together, however, they are a lethal combination—for governance as well as discovery.