Tag: phonons

• A microscope that catches the slightest hints of heat

  A superconducting transition-edge sensor (TES) is a device well-known for its extreme sensitivity to photons, the particles of light — so much so that they can count photons one by one. They also have very little noise, which makes their readings quite reliable. TESs are often used in single-photon detectors in quantum communications systems and in cryogenic bolometers (devices that measure infrared radiation) in astronomy. But for these virtues, however, engineers haven’t been able to use TES technology together with scanning-probe optics, where scientists use a physical probe to image surfaces at extremely high resolution. In atomic force microscopy, for example, a very sharp tip is mounted on a flexible cantilever over a surface to measure forces between the tip and the sample at the nanoscale. This technology gap has been important to fill because scanning-probe optics are currently limited by how sensitive detectors are to light fields just a few nanometres big. In other words, the missing piece was a device that married the sensitivity of a TES device with the ability of a scanning probe to access spatial scales of nanometres. A new effort by researchers from Singapore, Switzerland, and the US has offered to fill this gap using a bespoke new technique called bolometric superconducting optical nanoscopy (BOSON). According to the researchers, BOSON integrates a superconducting TES directly into a scanning near-field optical microscope. The findings were published in Physical Review X on July 25.

  ‘Near field’ has a simple meaning. In conventional microscopy, like the simple light microscope in a high-school biology lab, light from a sample is captured through lenses and eventually sent to the eyes of the observer. This is called far-field microscopy because the light that contains information about the sample under study travels several multiples of its wavelength before interacting with the detecting elements. In near-field microscopy, light travels much less than a single multiple of its wavelength before reaching these elements. For example, if the wavelength of the light is 500 nm, it may travel 5 cm — or 100,000-times its wavelength — before striking the lens. On the other hand, near-field microscopy, also called near-field nanoscopy, captures and analyses light that has travelled much less than 500 nm from the sample. Devices of this kind routinely use junctions made of graphene, semiconductors or metals to translate the properties of the light energy into a measurable electrical current. These technologies demand high optical power, in the milliwatt to sub-milliwatt range, as well as elaborate engineering. They also struggle to detect changes in a sample that produce weak electromagnetic fields, like vibrating atoms in some crystals. Graphene-based devices that reveal temperature changes in a sample by shifting their resistivity are also limited by the fact that graphene’s resistivity changes very weakly with temparature, limiting the devices’ usefulness in bolometry. The team behind the new study thus set about looking for a detector whose resistance would change abruptly with even a small thermal load. This was BOSON.

  At the heart of BOSON is a bridge. It’s made of niobium, a metal that becomes a superconductor at very low temperature. It’s also only 200-250 nm wide, a really small size that makes it extremely sensitive to heat. Imagine a single snowflake landing on your finger: even the gentle heat from your body suffices to melt it quickly. Similarly, even a small amount of heat will cause the niobium bridge’s temperature to rise enough to jerk it out of its superconducting state. The bridge sits between wider niobium leads. At the start of the researchers’ experiment, the team passed a constant current through the bridge. Hovering just above the bridge was the small, sharp tip of an atomic force microscope. When an infrared laser struck the probe tip, it concentrated the electromagnetic field onto the bridge. When the tip-induced field raised the electrons’ temperature by only a few millikelvin, a “hot spot” formed on the niobium bridge. In this region, the bridge resisted the flow of current enough for a voltage to register between the leads at the ends of the bridge. This voltage was the ultimate signal of interest, demonstrating that BOSON could reliably detect extremely small changes in temperature.

  The researchers also found that BOSON’s resolution is limited not by the size of the atomic force microscope’s tip (around 20 nm tip) but by the lengths across which the energy diffuses into the bridge — under 1 micrometre in the niobium bridge — and the size of the bridge itself. The researchers have written that further narrowing the bridge could further improve its spatial resolution.

  Still, to highlight BOSON’s optical reach in their study, they overlaid the bridge with a 50-nm thick flake of hexagonal boron nitride (hBN), a material known to contain an unusual kind of wave called hyperbolic phonon-polaritons when illuminated with mid-infrared light. Hyperbolic phonon-polaritons are formed from when photons interact strongly with vibrations in the grid of atoms in a crystal, especially when the vibrations are within a particular frequency range. This interaction allows light to be guided into tracks that are narrower than the diffraction limit — a very desirable ability in microscopes trying to achieve a high resolution. The team shone an infrared laser at the hBN crystal to produce hyperbolic phonon-polaritons, then monitored the niobium bridge. They found that the phonon-polaritons produced an electromagnetic field in the crystal and the bridge was sensitive to changes in this field even when the latter’s power was as feeble as 50 nanowatt — fully four orders of magnitude below the power required to draw the attention of existing near-field microscopes. According to the researchers, this dramatic advance stemmed from operating the detector exactly at its superconducting transition temperature, where the bridge’s sensitivity to temperature changes is highest. BOSON also revealed how the phonon-polaritons dispersed within the hBN crystal, found to be consistent with theoretical predictions. The team said that since the bridge width is the effective detector size, future bridges that are only tens of nanometres wide should be able to study materials like hBN with even more sensitivity.

  By combining a superconducting bolometer with a scanning probe, the team has shown that BOSON is a universal, cryogenic nano-optical detector whose sensitivity rivals the best available TES devices. The platform can reportedly detect weak shifts in the energy of a material with nanometre precision while depositing a negligible amount of energy into the sample, a feature that could prove useful in the study of quantum materials, which are typically very fragile. According to the team’s paper, an improved BOSON may in future may be able to detect single polaritons (quasiparticles each made of a photon coupled to an electric dipole) and be sensitive to electromagnetic fields with ultra-high frequencies (in the terahertz range). They’ve also speculated that thinner superconducting bridges and the use of improved techniques to sense voltage across them could make BOSON sensitive to power changes even slighter than nanowatts.

  Featured image: A schematic diagram of the experimental setup of BOSON. CP refers to ‘Cooper pairs’, which are the charge carriers in a superconductor. I_bias is the biasing current applied to the niobium bridge. Credit: Phys. Rev. X 15, 031027.

  2025.08.02

• Quasiparticles do the twist

  Physics often involves hidden surprises in how matter behaves at the smallest scales. A fundamental property in physics is angular momentum, which describes how things spin or rotate, from planets all the way down to particles. Angular momentum is involved in many important effects like magnetism and quantum states that could one day be used in quantum computers.

  When atoms vibrate inside crystals, the vibrational energy they release is often found in multiples of discrete values, i.e. they resemble fixed packets of energy. Physicists liken these packets to particles of vibrational energy that they call phonons.

  More particularly, a phonon is a kind of emergent particle called a quasiparticle. In 2017, Vijay B. Shenoy, an associate professor at the Centre for Condensed Matter Theory at the Indian Institute of Science, Bengaluru, explained the concept to me in a way I’ve always liked to return to:

  The idea of a ‘quasiparticle’ is a very subtle one. At the risk of being technical, let me try this: An excitation is called a particle if, for a given momentum of the excitation, there is a well-defined energy. Quite remarkably, this definition of a particle embodies what we conventionally think of as a particle: small hard things that move about.

  Now, to an example. Consider a system made of atoms at a very low density. It will be in a gaseous state. Due to their kinetic energy, the atoms will be freely moving about. Such a system has particle-like excitations. These particle-like excitations correspond to the behaviour of individual atoms.

  Now consider the system at a higher density. The atoms will be strongly interacting with each other and, therefore, make up a solid. You will never “see” these atoms as low-energy excitations. There will now be new types of excitations that are made of the collective motion of atoms and which will be particle-like (since there is a well-defined energy for a given momentum). These particle-like excitations are called phonons. Note that the phonon excitation is very different from the atom that makes up the solid. For example, phonons carry sound within a solid – but when the sound propagates, you don’t have atoms being carried from place to place!

  A ‘quasiparticle’ excitation is one that is very nearly a particle-like excitation: for the given momentum, it is a small spread of energy about some average value. The manifestation is such that, for practical purposes, if you watch this excitation over longer durations, it will behave like a particle in an experiment…

  Recently, physicists predicted that phonons can themselves carry angular momentum the way physical particles like electrons do. They were predicted to do so in materials called chiral crystals, where the atoms are arranged in a spiral structure. However, in spite of the exciting prediction, nobody had directly observed this phonon angular momentum before. Proof was missing in part because measuring something so small and subtle isn’t easy. A new study in Nature Physics finally appears to have fixed this gap, reporting the first direct evidence of the effect using a well-known chiral crystal.

  Researchers from Germany and the US designed an experiment with tellurium, an element whose crystals grow in spiral shapes that wind either to the left or to the right. Since phonons are the vibrations inside a crystal, their angular momentum as they travel in curved paths through the crystal can’t be recorded directly. Instead, the researchers surmised that if all the phonons in the chiral crystal added up, they might twist the whole crystal ever so slightly, like a wind-up toy.

  So in their experiment, they heated a crystal in an uneven way in order to throw the left‑ and right‑handed phonons off balance, leaving behind a net phonon angular momentum that the whole crystal would have to offset by twisting in the opposite direction.

  To test this, the team started by growing small, pure tellurium crystals in the lab, making sure some were single crystals — i.e. with all atoms lining up the same way — and others were polycrystals, consisting of atoms lining up in random orientations. The team assumed that only the pure chiral crystals would show the new effect whereas the polycrystals wouldn’t.

  Team members then attached the crystals to minuscule cantilevers. If the crystal twisted even a small amount, the cantilever would bend, and an electrical circuit would detect and amplify the signal. Finally, they created a temperature difference between the two ends of the crystals by shining a small, focused laser light on it. This thermal gradient was expected to allow a net angular momentum to build up, if it was there.

  The team ran its tests on both types of crystals, changing the direction of the temperature gradient and running the experiment at different temperatures. In the process the team also ruled out the effects of other forces acting on the crystals, such as expansion due to heating.

  When the laser was switched on, the single-crystal tellurium samples showed a clear torque on the cantilevers while the polycrystalline samples didn’t. The torque flipped direction if the temperature gradient was reversed — a smoking gun that it was related to the handedness of the vibrations — and disappeared altogether when the laser was turned off.

  The team measured the torque to be an extremely slight 10^-11 N·m, which matched theoretical predictions.

  At higher temperatures, even the pure crystals stopped displaying a torque, in keeping with the expectation that the effect only appeared below the Debye temperature — which is the temperature at which a crystal lattice has its highest vibrational quantum energy.

  More than the recent theoretical predictions, the research team’s motivation also traced back to an experiment that Albert Einstein and the Dutch physicist Wander Johannes de Haas conducted in 1915. It showed that flipping a magnetic field also made a tiny iron rod twist. Einstein and de Haas explained that this happened because the rod’s electrons had to conserve angular momentum, thus confirming that these particles had this property, an important moment in the history of physics. The researchers behind the new study similarly called what they observed the phonon Einstein-de Haas effect.

  Shenoy, however was more measured in his assessment of the new study:

  It is, in general, not unusual to have quasiparticles possessing properties of physical particles. Condensed matter physics is replete with examples, such as phonons (discussed here), magnons, density excitations in low dimensions, etc.

  What is not usual is the discussion of angular momentum in the context of phonons. As the authors emphasise, this is possible due to the noncentrosymmetric nature of tellurium. The system does not have centrosymmetry (or inversion symmetry): that is, roughly, if you flip [the crystal] ‘inside out’ it looks like an inside out image’ rather than itself. An instructive illustration is a mirror image: the mirror image of a circle is a circle (mirror-symmetric), but the mirror image of a right hand is not a right hand. Centrosymmetry is a three-dimensional version of mirror reflection. Broadly speaking, the whole report is not super surprising, but it is interesting that the scientists can measure this.

  Many of these physics papers reporting very specialised results make it a point to mention potential future applications of the underlying science. Admittedly, the pursuit of these applications, as and when they come to pass, and the commercial opportunities they create may help to fund the research. However, such speculation in papers also reinforces the idea that studies at the cutting edge are indebted (especially financially) to the future. I don’t agree with that position although I understand its grounding.

  For example, this is what the researchers behind the new study wrote in their paper (emphasis added; AM stands for ‘angular momentum’):

  … our measurements firmly establish the existence of phonon-AM in chiral crystals. Phonon-AM is the theoretical basis of chiral and topological phonons that may interact with topological fermions to create unique topological quantum states. Phonons can also transfer AM to other fundamental particles and elementary excitations allowing for novel quantum transduction mechanisms, thermal manipulation of spin, and detection of hidden quantum fields. This discovery provides a solid foundation for emergent chiral quantum states and opens a new avenue for phonon-AM enabled quantum information science and microelectronic applications.

  And this is what Shenoy had to say about that:

  I am not sure that [the finding] will have an immediate technological impact, particularly since this is a very subtle effect that requires very expensive single crystals; my guess is that this will be useful in some very specialised sensor application of some sort in the future. The authors also mention some microelectronics stuff, not sure about that. At this stage, this is firmly in the basic sciences column!

  2025.07.19

• Physicists produce video of time crystal in action 😱

  

  Have you heard of time crystals?

  A crystal is any object whose atoms are arranged in a fixed pattern in space, with the pattern repeating itself. So what we typically know to be crystals are really space crystals. We didn’t have to bother with the prefix because space crystals were the only kind of crystals we knew until time crystals came along.

  Time crystals are crystalline objects whose atoms exhibit behaviour that repeats itself in time, as periodic events. The atoms of a time crystal spin in a fixed and coordinated pattern, changing direction at fixed intervals.

  Physicists sometimes prefer to quantify these spin patterns as quasiparticles to simplify their calculations. Quasiparticles are not particles per se. To understand what they are, consider a popular one called phonons. Say you strike a metal spoon on the table, producing a mild ringing sound. This sound is the result of sound waves propagating through the metal’s grid of atoms, carrying vibrational energy. You could also understand each wave to be a particle instead, carrying the same amount of energy that each sound wave carries. These quasiparticles are called phonons.

  In the same way, patterns of spinning charged particles also carry some energy. Each electron in an atom, for example, generates a tiny magnetic field around itself as it spins. The directions in which the electrons in a material spin collectively determine many properties of the material’s macroscopic magnetic field. Sometimes, shifts in some electrons’ magnetic fields could set off a disturbance in the macroscopic field – like waves of magnetic energy rippling out. You could quantify these ‘spin waves’ in the form of quasiparticles called magnons. Note that magnons quantify spin waves; the waves themselves can be from electrons, ions or other charged particles.

  As quasiparticles, magnons behave like a class of particles called bosons – which are nature’s force-carriers. Photons are bosons that mediate the electromagnetic force; W and Z bosons mediate the weak nuclear force responsible for radioactivity; gluons mediate the strong nuclear force, which carries the energy you see released by nuclear weapons; scientists have hypothesised the existence of gravitons, for gravity, but haven’t found them yet. Like all bosons, magnons don’t obey Pauli’s exclusion principle and they can be made to form exotic states of matter like superfluids and Bose-Einstein condensates.

  Other quasiparticles include excitons and polarons (useful in the study of electronic circuits), plasmons (of plasma) and polaritons (of light-matter interactions).

  Physicist Frank Wilczek proposed the existence of time crystals in 2012. One reason time crystals are interesting to physicists is that they break time-translation symmetry in their ground state.

  This statement has two important parts. The first concerns time-translation symmetry-breaking. Scientists assume the laws of physics are the same in all directions – yet we still have objects like crystals, whose atoms are arranged in specific patterns that repeat themselves. Say the atoms of a crystal are arranged in a hexagonal pattern. If you kept the position of one atom fixed and rotated the atomic lattice around it or if you moved to the left or right of that atom, in both cases by an arbitrary amount, your view of the lattice will also change. This happens because crystals break spatial symmetry. Similarly, time symmetry is broken if an event repeats itself in time – like, say, a magnetic field whose structure changes between two shapes over and over.

  The second part of the statement concerns the (thermodynamic) ground state – the state of any quantum mechanical system when it has its lowest possible energy. (‘Quantum mechanical system’ is a generic term for any system – like a group of electrons – in which quantum mechanical effects have the dominant influence on the system’s state and behaviour. An example of a non-quantum-mechanical system is the Solar System, where gravity dominates.) Wilczek revived interest in time crystals as objects that break time-translation symmetry in their ground states. Put another way, they are quantum mechanical systems whose constituent particles perform a periodic activity without changing the overall energy of the system.

  The advent of quantum mechanics and relativity theory in the early 20th century alerted physicists to the existence of various symmetries and, through the work of Emmy Noether, their connection to different conservation laws. For example, a system in which the laws of nature were the same throughout history and will be in future – i.e. preserves time-translation symmetry – will also conserve energy. Does this mean time crystals violate the law of conservation of energy? No. The atoms’ or electrons’ spin is not the result of the electrons’ or atoms’ kinetic energy but is an inherent quantum mechanical property. This energy can’t be used to perform work the same way, say, a motor can pump water. The system’s total energy is still conserved.

  Now, physicists from Germany have reported that they have observed a time crystal ‘in action’ – a feat notable on three levels. First, it’s impressive that they have created a time crystal in the first place (even if they are not the first to do so). The researchers passed radio frequency waves through a strip of nickel-iron alloy a few micrometers wide. According to ScienceAlert, this ‘current’ “produced an oscillating magnetic field on the strip, with magnetic waves travelling onto it from both ends”. As a result, they “stimulated the magnons in the strip, and these moving magnons then condensed into a repeating pattern”.

  Second, while quasiparticles are not actual particles per se, they exhibit some properties of particles. One of them is scattering, like two billiard balls might bounce off each other to go off in different directions at different speeds. Similarly, the researchers created more magnons and scattered them off the magnons involved in the repeating pattern. The post-scatter magnons had a shorter wavelength than they did originally, in line with expectations, and the researchers also found that they could control this wavelength by adjusting the frequency of the stimulating radio waves.

  An ability to control such values often means the process could have an application. The ability to precisely manipulate systems involving the spin of electrons has evolved into a field called spintronics. Like electronics makes use of the electrical properties of subatomic particles, spintronics is expected to leverage spin-related properties and enable ultra-fast hard-drives and other technologies.

  Third, the researchers were able to produce a video showing the magnons moving around. This is remarkable because the thing that makes a time crystal so unique is the result of quantum mechanical processes, which are microscopic in nature. It’s not often that you can observe their effects on the macroscopic scale. The principal reason the researchers were able achieve this is feat is the method they used to create the time crystal.

  Previous efforts to create time crystals have used systems like quantum gases and Bose-Einstein condensates, both of which require sophisticated apparatuses to work with, in ultra-cold conditions, and whose behaviour researchers can track only by carefully measuring their physical and other properties. On the other hand, the current experiment works at room temperature and uses a more ‘straightforward’ setup that is also fairly large-scale – enough to be visible under an X-ray microscope.

  Working this microscope is no small feat, however. Charged particles emit radiation when they’re accelerated along a circular path. An accelerator called BESSY II in Berlin uses this principle to produce X-rays. Then the microscope, called MAXYMUS, focuses the X-rays onto an extremely small spot – a few nanometers wide – and “scans across the sample”, according to its official webpage. A “variety of X-ray detectors”, including a camera, observe how the X-rays interact with the sample to produce the final images. Here’s the resulting video of the time crystal, captured at 40 billion frames per second:

  I asked one of the paper’s coauthors, Joachim Gräfe, a research group leader in the department of modern magnetic systems at the Max Planck Institute for Intelligent Systems, Stuttgart, two follow-up questions. He was kind enough to reply in detail; his answers are reproduced in full below:

  1. A time crystal represents a system that breaks time translation symmetry in its ground state. When you use radio-frequency waves to stimulate the magnons in the nickel-iron alloy, the system is no longer in its ground state – right?

  The ground state debate is the interesting part of the discussion for theoreticians. Our paper is more about the experimental observation and an interaction towards a use case. It is argued that a time crystal cannot be a thermodynamic ground state. However, it is in a ground state in a periodically alternating potential, i.e. a dynamic ground state. The intriguing thing about time crystals is that they are in ground states in these periodically alternating potentials, but they do not/will not necessarily have the same periodicity as the alternating potential.

  The condensation of the magnonic time crystal is a ground state of the system in the presence of the RF field (the periodically alternating potential), but it will dissipate through damping when the RF field is switched off. However, even in a system without damping, it would not form without the RF field. It really needs the periodically alternating potential. It is really a requirement to have a dynamic system to have a time crystal. I hope I have not confused you more than before my answer. Time crystals are quite mind boggling. 😵🤯

  2. Previous experiments to observe time crystals in action have used sophisticated systems like quantum gases and Bose-Einstein condensates (BECs). Your experiment’s setup is a lot more straightforward, in a manner of speaking. Why do you think previous research teams didn’t just use your setup? Or does your setup have any particular difficulty that you overcame in the course of your study?

  Interesting question. With the benefit of hindsight: our time crystal is quite obvious, why didn’t anybody else do it? Magnons only recently have emerged … as a sandbox for bosonic quantum effects (indeed, you can show BEC and superfluidity for magnons as well). So it is quite straightforward to turn towards magnons as bosons for these studies. However, our X-ray microscope (at the synchrotron light source) was probably the only instrument at the time to have the required spatial and temporal resolution with magnetic contrast to shoot a video of the space-time crystal. Most other magnon detection methods (in the lab) are indirect and don’t yield such a nice video.

  On the other hand, I believe that the interesting thing about our paper is not that it was incredibly difficult to observe the space time crystal, but that it is rather simple to create one. Apparently, you can easily create a large (magnonic) space time crystal at room temperature and do something with it. Showing that it is easy to create a space time crystal opens this effect up for technological exploitation.

  2021.03.09

• Superconductivity: From Feshbach to Fermi

  (This post is continued from this one.)

  After a bit of searching on Wikipedia, I found that the fundamental philosophical underpinnings of superconductivity were to be found in a statistical concept called the Feshbach resonance. If I had to teach superconductivity to those who only knew of the phenomenon superfluously, that’s where I’d begin. So.

  Imagine a group of students who have gathered in a room to study together for a paper the next day. Usually, there is that one guy among them who will be hell-bent on gossiping more than studying, affecting the performance of the rest of the group. In fact, given sufficient time, the entire group’s interest will gradually shift in the direction of the gossip and away from its syllabus. The way to get the entire group back on track is to introduce a Feshbach resonance: cut the bond between the group’s interest and the entity causing the disruption. If done properly, the group will turn coherent in its interest and to focusing on studying for the paper.

  In multi-body systems, such as a conductor harboring electrons, the presence of a Feshbach resonance renders an internal degree of freedom independent of those coordinates “along” which dissociation is most like to occur. And in a superconductor, a Feshbach resonance results in each electron pairing up with another (i.e., electron-vibrations are quelled by eliminating thermal excitation) owing to both being influenced by an attractive potential that arises out of the electron’s interaction with the vibrating lattice.

  Feshbach resonance & BCS theory

  For particulate considerations, the lattice-vibrations are quantized in the form of hypothetical particles called phonons. As for why the Feshbach resonance must occur the way it does in a superconductor: that is the conclusion, rather implication, of the BCS theory formulated in 1957 by John Bardeen, Leon Neil Cooper, and John Robert Schrieffer.

  

  The BCS theory essentially treats electrons like rebellious, teenage kids (I must be getting old). As negatively charged electrons pass through the crystal lattice, they draw the positively charged nuclei toward themselves, creating an increase in the positive charge density in their vicinity that attracts more electrons in turn. The resulting electrostatic pull is stronger near nuclei and very weak at larger distances. The BCS theory states that two electrons that would otherwise repel each other will pair up in the face of such a unifying electrostatic potential, howsoever weak it is.

  This is something like rebellious teens who, in the face of a common enemy, will unite with each other no matter what the differences between them earlier were.

  Since electrons are fermions, they bow down to Pauli’s exclusion principle, which states that no two fermions may occupy the same quantum state. As each quantum state is defined by some specific combination of state variables called quantum numbers, at least one quantum number must differ between the two co-paired electrons.

  

  In the case of superconductors, this is particle spin: the electrons in the member-pair will have opposite spins. Further, once such unions have been achieved between different pairs of electrons, each pair becomes indistinguishable from the other, even in principle. Imagine: they are all electron-pairs with two opposing spins but with the same values for all other quantum numbers. Each pair, called a Cooper pair, is just the same as the next!

  Bose-Einstein condensates

  This unification results in the sea of electrons displaying many properties normally associated with Bose-Einstein condensates (BECs). In a BEC, the particles that attain the state of indistinguishability are bosons (particles with integer spin), not fermions (particles with half-integer spin). The phenomenon occurs at temperatures close to absolute zero and in the presence of an external confining potential, such as an electric field.

  

  Since bosons don’t follow Pauli’s exclusion principle, a major fraction of the indistinguishable entities in the condensate may and do occupy the same quantum state. This causes quantum mechanical effects to become apparent on a macroscopic scale.

  By extension, the formulation and conclusions of the BCS theory, alongside its success in supporting associated phenomena, imply that superconductivity may be a quantum phenomenon manifesting in a macroscopic scale.

  Note: If even one Cooper pair is “broken”, the superconducting state will be lost as the passage of electric current will be disrupted, and the condensate will dissolve into individual electrons, which means the energy required to break one Cooper pair is the same as the energy required to break the composition of the condensate. So thermal vibrations of the crystal lattice, usually weak, become insufficient to interrupt the flow of Cooper pairs, which is the flow of electrons.

  

  The Meissner effect

  In this context, the Meissner effect is simply an extrapolation of Lenz’s law but with zero electrical resistance.

  Lenz’s law states that the electromotive force (EMF) because of a current in a conductor acts in a direction that always resists a change in the magnetic flux that causes the EMF. In the absence of resistance, the magnetic fields due to electric currents at the surface of a superconductor cancel all magnetic fields inside the bulk of the material, effectively pushing magnetic field lines of an external magnetic potential outward. However, the Meissner effect manifests only when the externally applied field is weaker than a certain critical threshold: if it is stronger, then the superconductor returns to its conducting state.

  Now, there are a class of materials called Type II superconductors – as opposed to the Type I class described earlier – that only push some of the magnetic field outward, the rest remaining conserved inside the material in filaments while being surrounded by supercurrents. This state is called the vortex state, and its occurrence means the material can withstand much stronger magnetic fields and continue to remain superconducting while also exhibiting the hybrid Meissner effect.

  Temperature & superconductivity

  There are also a host of other effects that only superconductors can exhibit, including Cooper-pair tunneling, flux quantization, and the isotope effect, and it was by studying them that a strong relationship was observed between temperature and superconductivity in various forms.

  

  In fact, Bardeen, Cooper, and Schrieffer hit upon their eponymous theory after observing a band gap in the electronic spectra of superconductors. The electrons in any conductor can exist at specific energies, each well-defined. Electrons above a certain energy, usually in the valence band, become free to pass through the entire material instead of staying in motion around the nuclei, and are responsible for conduction.

  The trio observed that upon cooling the material to closer and closer to absolute zero, there was a curious gap in the energies at which electrons could be found in the material at a particular temperature. This meant that, at that temperature, the electrons were jumping from existing at one energy to existing at some other lower energy. The observation indicated that some form of condensation was occurring. However, a BEC was ruled out because of Pauli’s exclusion principle. At the same time, a BEC-like state had to have been achieved by the electrons.

  This temperature is called the transition temperature, and is the temperature below which a conductor transitions into its superconducting state, and Cooper pairs form, leading to the drop in the energy of each electron. Also, the differences in various properties of the material on either side of this threshold are also attributed to this temperature, including an important notion called the Fermi energy: it is the potential energy that any system possesses when all its thermal energy has been removed from it. This is a significant idea because it defines both the kind and amount of energy that a superconductor has to offer for an externally applied electric current.

  

  In simple terms, the density of various energy states of the electrons at the Fermi energy of a given material dictates the “breadth” of the band gap if the electron-phonon interaction energy were to be held fixed at some value: a direct proportionality. Thus, the value of the energy gap at absolute zero should be a fixed multiple of the value of the energy gap at the superconducting transition temperature (the multiplication factor was found to be 3.5 universally, irrespective of the material).

  Similarly, because of the suppression of thermal excitation (because of the low temperature), the heat capacity of the material reduces drastically at low temperatures, and vanishes below the transition temperature. However, just before hitting zero at the threshold, the heat capacity balloons up to beyond its original value, and then pops. It was found that the ballooned value was always 2.5 times the material’s normal heat capacity value… again, universally, irrespective of the material!

  The temperature-dependence of superconductors gains further importance with respect to applications and industrial deployment in the context of its possible occurring at higher temperatures. The low temperatures currently necessary eliminate thermal excitations, in the form of vibrations, of nuclei and almost entirely counter the possibility of electrons, or Cooper pairs, colliding into them.The low temperatures also assist in the flow of Cooper pairs as a superfluid apart from allowing for the energy of the superfluid being higher than the phononic energy of the lattice.

  However, to achieve all these states in order to turn a conductor into a superconductor at a higher temperature, a more definitive theory of superconductivity is required. One that allows for the conception of superconductivity that requires only certain internal conditions to prevail while the ambient temperature soars. The 1986-discovery of high-temperature superconductors in ceramics by Bednorz and Muller was the turning point. It started to displace the BCS theory which, physicists realized, doesn’t contain the necessary mechanisms for superconductivity to manifest itself in ceramics – insulators at room temperature – at temperatures as high as 125 K.

  A firmer description of superconductivity, therefore, still remains elusive. Its construction should not only pave the for one of the few phenomena that hardly appears in nature and natural processes to be fully understood, but also for its substitution against standard conductors that are responsible for lossy transmission and other such undesirable effects. After all, superconductors are the creation of humankind, and only by its hand while they ever be fully worked.

  Related articles

  • Stages of superconductivity: Researchers’ insight on ‘pseudogap’ an important advance (phys.org)

  2012.08.30