Molecular imaging – the in vivo visualization of cellular processes – is used extensively within preclinical research. Positron emission tomography (PET), single photon emission computed tomography (SPECT), fluorescence imaging and other techniques with a high sensitivity can all non-invasively image molecular targets in living animals, shedding light on the origins and mechanisms of disease, and enabling potential new therapies to be tested over time.
But can these advantages be translated from preclinical studies to a clinical setting? “We’ve been using imaging in preclinical modes for two decades – it’s now time to take what we’ve learned and translate it to the clinic,” says Christopher Contag, principal investigator of the Molecular Biophotonics and Imaging Laboratory at Stanford University in the US.
Early diagnosis of diseases like cancer is vital for improving treatment outcomes
Making an early diagnosis of diseases like cancer is vital for improving treatment outcomes. Almost all diseases begin with alterations at the cellular level, and detecting these earliest changes calls for imaging techniques with both high sensitivity and high resolution.
Unfortunately, most of today’s diagnostic tools can find only relatively large lesions. For example, magnetic resonance imaging (MRI) and X-ray computed tomography (CT) can detect tumours of approximately 1 cm3 in volume, equivalent to about one billion cells, while methods based on blood tests can detect about one million cells. Optical-imaging techniques such as fluorescence microscopy, on the other hand, can detect lesions as small as 0.001 mm3 – equivalent to about 1000 cells. “To improve early diagnosis, we need tools that can detect microscopic lesions,” Contag says.
Point-of-care diagnosis
So could optical techniques provide this desired early detection? Optical imaging certainly offers the necessary high resolution, but light cannot penetrate far into the body, which is a problem. While MRI and CT scan through the entire body, techniques such as white-light endoscopy can only image up to 1 cm beneath the surface of the body. Confocal microscopy, meanwhile, offers 1 μm resolution at depths of just 100 μm to 1 mm.
It should be possible, however, to exploit existing methods such as endoscopy to place the optical-imaging tools directly at the tissue surface and visualize early changes with microscopic resolution. This approach could shift diagnostic methods from “biopsy followed by histopathology” to non-invasive “point-of-care” diagnosis. “We’d like to provide the pathologist with an in vivo image that looks a lot like a stained-tissue image,” Contag explains.
To do this, the Stanford team has developed a miniaturized dual-axis confocal fluorescence microscope with a MEMS (microelectromechanical systems)-based scanning core. The researchers showed that the microscope, which is small enough to fit inside the instrument channel of a standard endoscope, could image the junction between Barrett’s oesophagus (a condition that increases the risk of oesophageal cancer) and normal cells. This junction is currently detected by taking biopsies in random suspect areas; in vivo imaging could instead accurately reveal where best to biopsy.
The team is now testing the miniaturized microscopes in the clinic to image oesophageal and colon cancer, using topical indocyanine green (ICG) as a contrast agent. ICG acts as both a colorimetric and a fluorescent contrast, enabling simultaneous macroscopic viewing and microscopic imaging with 3–5 μm resolution.
Contag and colleagues have made several modifications to the original microscope design, including stitching together overlapping image frames in real time to increase the field of view. They have also redesigned the device to perform 3D imaging by using two MEMS mirrors to scan in the x–y and z directions – enabling scanning of a 300 μm3 volume in a second or two.
Fluorescence imaging is ideal for detecting multiple probes, each emitting light at a different wavelength, at the same time. This “multiplexed” approach can provide information on both the molecular content and environment of the tissue, and enable endoscopists to rapidly distinguish between normal and precancerous tissues. The Stanford team demonstrated multispectral functionality of the dual-axis microscope by imaging multiple molecular probes that emit in the 500–800 nm range.
Fluorescence imaging enables multiplexing with four or five different fluorophores, but as this number increases it becomes more likely that the signal from one fluorescent dye will overlap with adjacent channels. Ideally, says Contag, a diagnostic system should use nearer to a dozen different channels. To achieve this, the researchers turned their attention to surface-enhanced Raman spectroscopy (SERS) using functionalized SERS nanoparticles as molecular-imaging contrast agents.
Research team Christopher Contag (front row, far right) and colleagues at Stanford University’s Molecular Biophotonics and Imaging Laboratory. (Courtesy: Christopher Contag)
These nanoparticles have a layer of Raman-active molecules adsorbed onto a gold core (which acts to significantly enhance the Raman signal) and are coated with a silica layer functionalized with a variety of tumour-targeting agents. By using different Raman-active molecules, each nanoparticle type generates a unique Raman spectral signature, enabling high levels of multiplexing.
To perform in vivo SERS, Contag’s team needed to miniaturize a Raman microscope to create an endoscopic probe. Designing a device for colon-cancer screening, the researchers developed a non-contact, 5.3 mm diameter Raman scanning probe that can scan the entire colon in less than 10 minutes. The probe’s rotating fibre-bundle tip contains an illumination fibre surrounded by 36 collection fibres that direct the Raman signals onto a CCD camera. The spectra are then resolved into individual Raman fingerprints.
For clinical application, the scanning procedure will involve using the endoscope to spray tumour-targeted SERS nanoparticles onto the area of interest during endoscopy. Any unbound particles are washed off prior to scanning and spectral analysis can be performed in real time to determine the presence of any pathological conditions.
In tests on a hollow 5 cm cylindrical phantom (a tissue substitute), the scanning Raman probe could detect particles of different types placed on its inside surface. In further tests on human colon tissue, the device could accurately identify 10 different types of SERS nanoparticle applied to the tissue samples. Furthermore, using known reference spectra, the system was able to separate individual Raman spectra from a mixture of particle types.
The team is also investigating the application of real-time “ratiometric” imaging, in which the relative concentrations of two or more nanoparticle types are determined, with one type serving as a non-targeted control and the other(s) used to target relevant cells. By accounting for any non-specific particle accumulation after washing, as well as for variable working distances, this approach improves the specific detection of bound, targeted nanoparticles. Tests on colon-tissue samples showed detection of picomolar concentrations of SERS nanoparticles, with analytical calculations predicting a detection limit of just 56 nanoparticles per cell.
Contag notes that the nanoparticles have not been tested in humans yet, but says that discussions to do so are ongoing with the US Food and Drug Administration. In the meantime, the team is refining its kit further. For example, his team has already introduced a built-in microsurgical tool – a pulsed electron avalanche knife – that can excise a small cylinder of tissue if disease is detected.
The researchers are also continuing to progress their fluorescence-based dual-axis confocal microscope for applications including visualization of circulating tumour cells in the blood. Other developments include extending optical-imaging approaches to other sites, such as additional hollow organs, accessible organs like the skin and oropharynx, and surgically accessed organs such as the prostate, ovaries, breast or brain.
A schematic of the prosthetic vision system developed by Daniel Palanker. (Courtesy: Daniel Palanker)
By Margaret Harris at the AAAS meeting in San Jose
“Restoration of sight to the blind” is a brave claim, one with an almost Biblical ring to it. For Daniel Palanker, though, it is beginning to look as if it is an achievable goal. A medical physicist at the University of Stanford, Palanker has developed a prosthetic vision system that replaces damaged photoreceptors in the retina with an array of tiny photodiodes. When infrared images are projected onto this array, the photodiodes convert the light pulses into electrical signals, which are then picked up by the neurons behind the retina and transmitted to the brain. The result is an artificially induced visual response that, while not as good as normal vision, could nevertheless provide “highly functional restoration of sight” to people with conditions such as retinitis pigmentosa or age-related macular degeneration (AMD).
A moderately realistic, gravitationally lensed accretion disc around a black hole, created by Double Negative artists. (Courtesy: Classical and Quantum Gravity)
In recent years, science and science fiction have come together in cinema to produce a host of rather spectacular visual treats, the best of the lot being Christopher Nolan’s epic Oscar-nominated film Interstellar. That actual science has played a major role in film is pretty well known, thanks to the involvement of theoretical physicist Kip Thorne, who was an executive producer for the project. But in a near-cinematic plot twist, it has emerged that Thorne’s work on trying to develop the most accurate and realistic view of a supermassive black hole “Gargantua” has provided unprecedented insights into the immense gravitational-lensing effects that would emerge if we were to view such a stellar behemoth.
To produce the awe-inspiring images of the wormhole and Gargantua that audiences across the globe marvelled at late last year, Thorne and a team from the acclaimed London-based visual effects company Double Negative developed a new computer code dubbed “Double Negative Gravitational Rendered” and have now published a paper detailing their work in the journal Classical and Quantum Gravity, which is published by IOP Publishing, which also publishes physicsworld.com.
Instead of focusing how individual rays of light would be distorted by the black hole, the code aims to solve the equations for how bundles of light (light beams) would navigate the extreme warped space–time structure that would surround the spinning Kerr black hole that is Gargantua. This was done to get rid of some of the strange visual anomalies that the team saw early on in its work. The team saw distant flickering stars and nebulae that would rapidly move across the screen if the standard approach of using just one light ray per pixel in the code was applied, which in the case of an IMAX image would amount to a total of 23 million pixels.
“To get rid of the flickering and produce realistically smooth pictures for the movie, we changed our code in a manner that has never been done before,” says Oliver James, chief scientist at Double Negative, explaining that once the code “was mature and creating the images you see in the movie Interstellar, we realized we had a tool that could easily be adapted for scientific research”.
They also found that the dragged space–time and the lensing would mean that an observer or a camera would see the accretion disc that surrounds Gargantua wrapped over and under the black hole’s shadow and that distant stars would move in a complex swirling dance around the hole as the camera orbits it. Indeed, thanks to a curious optical effect know as a “caustic” or a “caustic curve”, the images of the stars or nebulae would get amplified and split into double or even multiple images or even cancel in a flash of light.
To learn a bit more about these curious caustics (hint: they are actually pretty common and you have seen one in action if you have seen a rainbow), find out about how Gargantua was made to bend the rules of physics for a good cause and look into the perfect Einstein rings that emerge in the team’s simulations, delve into the paper’s depths. In the meanwhile, do be sure to read my review of Interstellar (warning: it contains spoilers!) as well as Thorne’s book The Science of Interstellar.
Are you tired of the same old boiled egg staring up at you every morning? Then why not try this simple trick from the Japanese chef Yama Chaahan, who in the video above creates a boiled egg with the yolk on the outside and the white in the middle. There is angular momentum and fluid dynamics involved, and if you don’t understand Japanese, the Huffington Post has a step-by-step guide in English.
After two days of getting to grips with biophysics – see here and here for my experiences – I was ready for a change of scene. And a visit to the Space Telescope Science Institute (STScI), co-located with the Johns Hopkins University in Baltimore but operated on behalf of NASA, was just what I needed.
The STScI is home to many of the scientists and engineers who made the Hubble Space Telescope possible, and who have been working for many years to design the optics and instrumentation for its successor – the James Webb Space Telescope (JWST), which is due to be launched in 2018. The institute also runs the science operations for Hubble and soon will for the JWST, providing software tools for astronomers to make their observations and processing the raw data acquired by the onboard instruments to make it ready for scientific analysis.
A new technique for cooling a macroscopic object with laser light has been demonstrated by a team of physicists in Germany and Russia. Making clever use of the noise in an optical cavity, which normally heats an object up, the technique could lead to the development of “stable optical springs” that would boost the sensitivity of gravitational-wave detectors. It could also be used to create large quantum-mechanical oscillators for studying the quantum properties of macroscopic objects or to create components for quantum computers.
Physicists already have ways of cooling tiny mirrors by placing them in an optical cavity containing laser light. When the mirror is warm, it vibrates – creating a series of “sidebands” that resonate with light at certain frequencies. The first lower sideband has a frequency equal to the difference between the resonant frequency of the cavity and the vibrational frequency of the mirror. So when a photon at that frequency enters the cavity, it can be absorbed and re-emitted with an extra quantum of vibrational energy. As a result of this “dispersive coupling” process, the mirror cools because energy from it is removed.
Dispersive coupling works best when the bandwidth of the cavity is much smaller than the vibrational frequency of the mirror. This is possible for relatively small mirrors with vibrational frequencies in the hundreds of megahertz. However, for more massive mirrors with vibrational frequencies in the hundreds of kilohertz, optical cavities with sufficiently narrow bandwidths are simply not available.
Cooling with noise
In this latest work, a large object was cooled using a new technique that involves “dissipative coupling” as well as dispersive coupling. Dissipative coupling was first proposed in 2009 by Florian Elste and Aashish Clerk of McGill University and Steven Girvin at Yale University. It makes clever use of quantum “shot noise” in laser light, which would normally be absorbed by the mirror and cause it to heat up.
However, if the mirror is in an optical cavity and its motion couples to the mirror’s reflectivity in just the right way, then there are two ways that the noise can reach the mirror: it can travel directly from the laser to the mirror or it can bounce around the cavity before driving the mirror. Just as in an interferometer, noise taking these two paths can interfere destructively or constructively.
Clerk and colleagues realized that the system can be set up so that destructive interference stops this quantum noise from heating the mirror but does not prevent the mirror from losing energy to the noise. The net effect is a strong cooling of the mirror’s motion, which could in principle take the mirror to its quantum ground state. “Unlike standard cavity cooling schemes, this interference doesn’t rely on having a very large mechanical frequency,” explains Clerk – meaning that it can be used to cool large mirrors that have low vibrational frequencies.
Couplings working together
In the latest work, Roman Schnabel and colleagues at the Max Planck Institute for Gravitational Physics in Hannover, Moscow State University and the Leibniz University of Hannover have now shown that dissipative and dispersive coupling can work together to cool relatively large mirrors. Based on an idea first proposed by the researchers in 2013, the technique uses a cavity created by a Michelson–Sagnac interferometer (see figure).
What they have done is to fire laser light at a beamsplitter to create two beams that go off at right angles to each other. These beams then bounce off two mirrors, making their paths form a right-angled triangle. Light from the output port of the interferometer is sent to a “signal-recycling mirror”, or SRM, where some of the light is reflected back into the interferometer and some is sent to a detector. The optical cavity is fine-tuned by adjusting the position of the SRM, while the cavity properties are monitored using a frequency analyser connected to the detector.
The object to be cooled is a silicon-nitride mirror just 40 nm thick, which is placed at the centre of the cavity. The mirror is about 1.2 mm across, weighs 80 ng and has a fundamental vibrational frequency of 136 kHz. The vibrational motion of the mirror changes not only the resonant frequency of the cavity – leading to the emergence of sidebands and dispersive cooling – but also the bandwidth of the cavity. When the rate of change of the bandwidth is large, energy can be exchanged between the cavity and the mirror. By carefully adjusting the phase between the vibrating mirror and the light, energy alone will flow from the mirror to the cavity, thereby cooling the mirror.
Sub-kelvin cooling
The researchers monitored the temperature of the mirror by using the laser light to measure its motion. They found that by using a combination of dispersive and dissipative cooling, they could cool the mirror from room temperature to 126 mK. Commenting on the experiment, Clerk told physicsworld.com that “Schnabel’s is the first experimental system where you have the special kind of dissipative optomechanical coupling that can let you do something truly new”.
One possible application of the technique is to use it to cool relatively large objects to their quantum ground states of vibration. Such quantum oscillators would comprise billions of atoms and could be used as “Schrödinger’s cats” to study quantum mechanics on a macroscopic scale. Other applications include using such quantum oscillators as components in quantum computers and other quantum-information systems.
Stabilizing an optical spring
However, it is not the cooling power of the technique that most interests Schnabel and colleagues. Schnabel told physicsworld.com that the demonstration is a proof-of-principle of their model of how light interacts with an oscillating mirror within a gravitational-wave detector. Their goal is to create a “stable optical spring” whereby a mirror in a huge interferometer undergoes a stable oscillation when laser light is shone on it. A gravitational wave travelling through the mirror would cause a tiny disruption in the oscillation, which would be detected by the interferometer. The problem is that noise in the system heats the mirror and causes it to vibrate erratically. This makes the measurement extremely difficult in existing set-ups.
“Our goal is to avoid uncontrolled heating of the mirror,” explains Schnabel, who says that the team will now use the model to try to create a stable optical spring using a 100 g pendulum as a mirror in a small interferometer. The ultimate goal of the research is use a mirror of about 40 kg for use in gravitational-wave detectors of the future.
Is there a limit on how large a quantum superposition can be or can macroscopic objects, such as humans or say cats, also exist in a superposition of quantum states? Our daily experience seems to suggest that large objects do not obey the rules of quantum mechanics and are said to behave classically. This suggests that there could be a fundamental boundary between the quantum and classical worlds.
To try and nail down exactly where this boundary lies, researchers in Germany have tracked the motion of a large atom in an optical lattice. They found that the atom moves in a non-classical way, behaving as a quantum superposition that occupies more than one location at any given time.
Boundary conditions
Probing the classical–quantum boundary is currently of great interest to physicists, with a variety of different experiments trying to work out where such a cut-off may lie. Indeed, in the past few years, physicists have been placing ever-larger objects into states of quantum superposition. These are often interference experiments, whereby large molecules are sent through a double slit and made to interfere with themselves.
But in 1985 Anthony Leggett and Anupam Garg took a decidedly different approach to the quest by developing a theory known as “macrorealism”. Instead of showing that quantum theory holds, they aimed to show that anything apart from a quantum description would disagree with experimental observations. In explicit contrast with quantum theory, the theorists posited that in the worldview of macroscopic realism, large objects must be in one determinate macroscopic state at any given time, allowing for no superposition or blurriness in the system. Macrorealism has two main criteria: that macroscopic superpositions are not allowed and that it is possible to make a measurement of the system without influencing the system in any way, meaning that you can always measure, say, the location of a large object without disturbing it.
If macrorealism were true, repeated measurements, at different times, of a single macroscopic system would only be statistically correlated up to a certain degree, giving what they called the Leggett–Garg (LG) inequality. The aim then was to violate the inequality with experimental evidence. This is similar to the Bell inequalities, which set out to show that another basic quantum effect, known as entanglement, is indeed possible. The difference is that for Bell’s inequalities, the measurements are made at different points in space, while for the LG inequality, the experiments take place at different times. Over the years, a number of experiments on photons, nuclear spins and superconducting circuits have been carried out to violate the LG inequality.
Walk the line
“According to [macrorealism], the [object] always moves on a specific trajectory, independent of our observation,” says Andrea Alberti at the University of Bonn, Germany, explaining “The challenge was to develop a measurement scheme of the atoms’ positions which allows one to falsify macro-realistic theories.” Alberti, along with Carsten Robens also at Bonn and colleagues in the UK, has violated the LG inequality with the largest quantum objects to date. The team observed the random quantum walk of a caesium atom in an optical lattice and used a certain type of “non-invasive” measurement that gives the most stringent violation of the inequality.
In an almost perfectly contrary manner to its classical cousin, a particle in a quantum random walk simultaneously travels in both directions – a “coherent superposition” of right and left. Over many steps, the particle is thought to be “delocalized” or blurred over many positions. Previously, researchers have seen the quantum random walk of a caesium atom. In this new work, the atom moves along one of two optical standing waves that have opposite electric-field polarizations. As it travels, the atom’s position is measured at various times, with the aim of measuring a correlation between the temporally separated positions.
To do this, the team begins by putting the atom into a superposition of two internal hyperfine spin states – this corresponds to being in both waves simultaneously. Next, the two optical waves are made to slide past each other and this makes the atom smear out or blur over a distance of up to about 2 µm – this is the quantum walk. The atom is then optically excited, and its subsequent fluorescence reveals its final location.
Cat or no cat?
Through the experiment, the researchers make three consecutive measurements. The first and the third are known – they know where the atom began its walk from, and thanks to the florescence, they known the final position. The middle measurements, which determine the internal spin-state of the atom are done non-invasively – if the atom is in one state – say, spin-up – then it is noted, but nothing is done to the experiment. If, instead, it is in spin-down state, it is transported far off so that its further evolution until the final position measurement is made cannot possibly influence the evolution of a particle that was left undisturbed. If the atom then fails to light up when the final fluorescence measurement is made, we know that the atom was in the spin-down state and was therefore discarded.
Hidden-cat null-measurement protocol: the Bonn team has developed a measurement scheme that indirectly measures the position of an atom. In essence, one looks where the caesium atom is not. The image clarifies this procedure. Let us assume that two containers are in front of us and a cat is hidden under one of them (a). However, we do not know which one. We tentatively lift the right container (b) and we find it empty. We thus conclude that the cat must be in the left container and we have not disturbed it. Had we have lifted the left container instead, we would have disturbed the cat (c), and the measurement would have to be discarded. (Courtesy: Andrea Alberti/www.warrenphotographic.co.uk)
A simple way to imagine this set-up is to imagine a guessing game wherein you have two containers and under one of them is a cat. If lifting up one container reveals it is empty, we can assume that the cat is undisturbed in the second container – this is synonymous to the spin-up state. Any measurement result where the cat is seen in the container (i.e. the spin-down state) is moved away or “discarded”.
By carrying out this “null result” measurement technique in the middle step, the researchers could determine the atom’s location without directly interacting with it. By repeating this experiment many times, and seeing when the fluorescence is detected, the researchers can tell which wave the atom was in (and therefore its position) and also that the atom was not disturbed in any way. If macrorealism was true, the null measurement would not affect the outcome of the final fluorescence measurement, and the total amount of correlation of the atom’s position in time could be explained classically – but this is not the case. Indeed, the blurring that happens in the quantum walk leads to a stronger total correlation than is possible under macrorealism. This is mathematically demonstrated via the LG inequality violation, clearly showing that macrorealism cannot apply to the caesium atom.
Rainer Kaltenbaek of the Quantum Foundations and Quantum Information group at the University of Vienna, who was not involved in the current work, found the work interesting. He points out that while the superpositions created by the team were not very massive (as compared with some other experiments) they are still relatively large, being on the scale of 2 µm. This might seem tiny, but it is comparable to a human hair, which is about 75 µm across, while most bacteria are around 3 µm. Kaltenbaek also points out that “quantum physics does not perceive the [null measurement] as really ‘non-invasive’… it’s only non-invasive from a ‘realistic’ point of view.” He continues, “The authors state in their conclusions that one can still stick to a ‘realistic’ picture if one does not mind nonlocality – Bohmian mechanics is an example of that. Of course, that comes at a price – one runs into difficulties as soon as one starts thinking about relativity where ‘nonlocality’ and ‘simultaneous’ effects do not work out as nicely as in non-relativistic physics.”
The results of Alberti’s experiment seem to nail down for sure that a caesium atom obeys the laws of quantum mechanics, and that macrorealism does not apply. In the future, similar experiments with even larger masses and with longer superposition times will help to either narrow down the inherent boundary that lies between the quantum and classical world, or banish it once and for all and lay the foundations for a more advanced quantum theory.
The International Year of Light is a global celebration, but right now, it’s definitely got its heart in San Francisco. For the past five days, experts in optics, lasers and biomedical imaging have been converging on the “city by the bay” for the annual Photonics West conference, and I’ve joined them in order to learn more about the hot topics in optical science.
In ancient history, the Bronze Age was followed by the Iron Age, as humans learned to make tools that were harder and more durable than those their ancestors had crafted from copper-based alloys. So when a new family of superconducting materials based on iron, rather than copper, was reported in early 2008, headline-writers were quick to announce the beginning of the “Iron Age” of superconductors.
The discovery was certainly a surprise. Iron-based materials are usually associated with magnetism, not superconductivity (the phenomenon where electrical current flows without resistance), although elemental iron can, under high pressure, become superconducting at very low temperatures. In addition, the chemical properties of the new iron-based superconductors (Fe SCs) were very different from those of the superconductors that contain copper, which are known collectively as cuprates. To physicists, this suggested that the mechanism behind superconductivity in Fe SCs must be different from the mechanism that produces superconducting behaviour in other materials.
Now, seven years later, we may be in a position to ask how Fe SCs are developing in comparison to the older members of the superconducting family – particularly the cuprates, which are sometimes called “high-temperature superconductors” because they become superconducting when cooled below a transition temperature, Tc, that in some cases exceeds 90 K. This is an important asset because their Tc is above the boiling temperature of liquid nitrogen, 77 K, which means that cuprates can be made to superconduct in systems that use liquid nitrogen rather than more expensive liquid helium as a coolant. Indeed, cuprate superconductors already have several applications (including superconducting quantum interference devices, or SQUIDs, which can detect extremely minute magnetic fields) and they are beginning to be applied on larger scales as well – for example in superconducting leads already being used in CERN’s Large Hadron Collider. The question we want to ask is: how will Fe SCs stack up against their increasingly useful predecessors?
Physics and chemistry together
Superconductivity is so fascinating and puzzling a phenomenon that it took almost 50 years from its discovery in the early 20th century until a theory that explains its mechanism was formulated. This theory, which is called “BCS” after its discoverers John Bardeen, Leon Cooper and Robert Schrieffer, is now firmly established, having celebrated its half-centenary a few years ago. The discovery of high-temperature cuprate superconductivity in 1986 was a kind of second revolution in the history of superconductivity, and one lesson we have learned from it is that physics and chemistry have to be “married”. In other words, quantum chemistry, like it or not, lies at the heart of the high-Tc cuprates’ crystal and electronic structures. So if we want to understand the mechanism for superconductivity in these materials, or to explore the design of new ones, we need to understand their chemistry.
1 Iron versus copper
Comparing the (a) typical crystal structure, (b) Fermi surface and (c) superconducting gap in momentum space of the iron-based (left) and cuprate (right) superconductors.
In the cuprates, superconducting currents, or “supercurrents”, flow along the copper-oxide planar crystal structures shown in figure 1a. Fe SCs also have a planar structure, but in their case, the key, current-carrying plane comprises compounds of iron and, typically, elements found in column 15 of the periodic table, such as arsenic. Elements in this column are called “pnictogens”, which is why Fe SCs are sometimes called iron-pnictides. While cuprates have some chemical variability, the variety seen in the Fe SCs is even greater. In the former, there are basically only two “families” of compounds, represented by La2CuO4 and YBa2Cu3O7. In these compounds, carriers of supercurrents can be prepared by, for example, reducing the number of oxygen atoms (a process called doping). In the Fe SCs, by comparison, there are several different families. The first material discovered (by one of us, HH) was a four-element compound, LaFeAsO, which is called “1111” in the jargon. Since then, it has been joined by several other families, from “122” down to “11” (figure 2).
2 The iron families
Crystal structures of four “families” of iron-based superconductors, showing the positions of iron atoms (brown), pnictogen atoms (green, labelled Pn) and chalcogen atoms (green, labelled Ch) in each family. The positions of alkali atoms (A), alkaline-earth atoms (Ae) and other elements present in the “111”, “122” and “1111” families are also shown.
The chemical diversity of the Fe SCs matters because their Tc and the way in which superconductivity emerges both depend not only on which family a superconductor belongs to, but also on the chemical compositions even within one family. This may sound like too complex chemistry, but on the other hand, those of us who study superconductivity have now had more than a quarter of a century to get used to complicated compounds such as Sr14–xCaxCu24O41 (which is known, jokingly, as the “telephone directory cuprate”). This cuprate potentially harbours, due to its peculiar crystal structure, some interesting physics. So the lesson is: do not be afraid of chemistry.
Another lesson that applies to both iron-based and cuprate superconductors is that it pays to look out for unexpected things. In fact, when HH discovered the first iron-pnictide, he was not actually aiming to find new superconductors at all. Instead, in 2005 his group at the Tokyo Institute of Technology was exploring magnetic semiconductors to build on their earlier discovery of transparent p-type conductors in compounds with the chemical formula LaCuChO. In this compound, the symbol “Ch” is either sulphur or selenium, and copper is in its +1 oxidation state. HH then moved on to a slightly different system, LaTMPnO, where “TM” is a transition metal with an unfilled orbital in the 3d electron shell (such as iron) and “Pn” is a pnictide (either phosphorus or arsenic). This system seemed interesting because it has the same crystal structure as LaCuChO, yet the transition metal in it is in a +2 oxidation state. This implies a tendency towards magnetism, where each transition-metal atom has an open-shell electronic configuration and the total electron spin tends to be non-zero.
The surprise came in 2006 when not only magnetism but also superconductivity emerged in LaFePO, though with Tc = 4 K (as discovered by HH in collaboration with Yoichi Kamihara and colleagues), and in LaNiPO, where Tc= 3 K. The big breakthrough came in early 2008 when it was reported that an arsenic compound doped with fluorine, LaFeAsO1–xFx, was found to have a significantly higher Tcof 26 K. Soon afterwards, a group of researchers in China found that Tc in this compound can be raised to 55 K when lanthanum is replaced with samarium.
Theorists catch up
Right after the discovery of the “1111” superconductivity, one of us (HA), in collaboration with Kazuhiko Kuroki and others, constructed a theory to explain how superconductivity operates in Fe SCs. Another group, including Igor Mazin, David Singh and colleagues, independently developed a similar theory at the same time. We started with an observation from the periodic table of the elements. Each transition-metal atom has electrons in its d-orbitals, which have an angular momentum of 2ℏ. As you move along the rows in this part of the periodic table, the number of filled or part-filled d-orbitals increases up to a maximum of 10 (recall that there can be up to two electrons per orbital, one spin up and one spin down, as dictated by the Pauli exclusion principle). Copper, located at the far right of the transition-metal part of the periodic table, has nine electrons in its five 3d orbitals in the cuprates where copper has +2 ionic state, which leaves one orbital unfilled – and thus only one of its d-orbitals is left chemically active.
For copper atoms in the cuprate superconductors, it is this single unfilled orbital that carries the supercurrent. By contrast, iron sits around the middle of the periodic table and thus has more than one chemically active d-orbital (typically three). This implies that iron has a very “open shell” configuration, with only about half of its five d-orbitals filled. Hence, the supercurrent in iron-based superconductors must be carried by electrons in multiple d-orbitals.
To understand what these superconducting electrons are doing (and thus better understand how the cuprates and Fe SCs differ from each other), physicists employ a concept called a Fermi surface. Quantum mechanically speaking, the electrons in a metal are described by wavefunctions in a given crystal, with up to two electrons for each wavefunction (again due to Pauli’s exclusion principle). These wavefunctions will be accommodated in orbitals up to a certain highest energy, called the Fermi energy. In momentum space, the equi-energy contour forms what is called a Fermi surface, and the shape of this surface can tell us a lot about superconducting behaviour. In cuprate superconductors, for example, the Fermi surface is very simple (and simply connected as well), due to the single-orbital character of its electron configuration (figure 1b). For the Fe SCs, though, the Fermi surface is a composite of multiple surfaces, due to its multi-orbital character. Consequently, the Fermi surface of iron-based superconductors comprises multiple “pockets”.
If you open any textbook of condensed-matter physics, you will read that superconductivity (as revealed by BCS theory) arises when electrons around the Fermi energy pair up. The formation of these “Cooper pairs” is possible because a coupling between electrons and phonons (the quantum-mechanical version of vibrations of a crystal lattice) produces a slight attraction between electrons, on top of the repulsion they experience due to having the same electric charge. The superconducting BCS state, composed of Cooper pairs, has a lower energy than unpaired electrons, and this energy gain produces a gap (called the BCS gap) just above the Fermi energy. More importantly, the BCS state harbours a spontaneous breaking of a symmetry (gauge symmetry, to be precise), which causes current to flow without resistance.
That explanation works well for conventional superconductors, but the discovery of high-Tc superconductivity in the cuprates made physicists realize that superconductivity can also arise from electron–electron repulsion per se, which is strong for transition elements. In this case, the pairing is mediated by fluctuations in spin structure rather than the lattice vibration. Another essential difference is that, while pairs of electrons in conventional superconductors have a relative angular momentum of zero (which is dubbed an “s-wave pairing”), in the cuprates we have pairs of electrons circulating each other with a non-zero angular momentum of 2ℏ (a “d-wave pairing”). Under these circumstances, the BCS gap – which is usually entirely positive – changes its sign. Namely, if you imagine walking along the Fermi surface for cuprate superconductors, you will see the gap changes its sign twice (figure 1c).
This is interesting, but the BCS gap has to vanish across the sign-changing points, or nodes, in a continuous fashion, which makes the overall magnitude of the BCS gap smaller, ending up with rather low Tc. In the cuprates, we cannot evade this: the nodes have to exist, because the nodes must intersect the simply connected Fermi surface at some point. For Fermi surfaces that are multiply connected, on the other hand, the sign-changing lines could lie in-between the pockets, thus giving us one pocket with an entirely positive BCS gap while the other pocket has an entirely negative gap. This clever pairing is called sign-reversing s-wave, or s±, and it seems to be happening in Fe SCs of the “1111” type. In fact, there is now a body of experimental results to support this theory.
3 Uemura plot
Transition temperature Tc for various superconducting materials plotted against their Fermi temperature TF (estimated from superfluid densities) on a double-logarithmic scale. Iron-based superconductors (Fe SCs) are here represented by compounds BaFe2(As1–xPx)2, as its phosphorus content x increases (red circles) or decreases (red squares) from x = 0.30.The cuprates are represented by green diamonds, green squares and green triangles (showing three different families). Both Fe SCs and cuprates are found near the top perimeter of the plot. Also plotted here are other classes of unconventional superconductors, including organic superconductors (purple triangles), a cobalt compound (green cross), the so-called heavy-fermion compounds that contain uranium atoms (black stars) and compounds containing carbon and alkali atoms (blue crosses) as well as the conventional low-Tc superconductors such as elemental Nb (inverted blue triangles) for comparison. We have also included, as guides, a blue line representing TF and a dashed line representing transition temperature, TB, for the Bose–Einstein condensation that a system with a given TF would have if the Cooper pairs were pure bosons.
Since Tc is in general governed by the underlying electron energy scale, it is useful to look not only at the absolute value of Tc, but also at the relationship between Tc and the Fermi temperature TF (which is just the Fermi energy translated into temperature). If we follow Yasutomo Uemura and plot the experimental Tc for known superconductors against TF, we can see that Tc for known superconductors basically scales with TF (figure 3). In addition, we can also see that the Fe SCs are situated around the topmost perimeter of the plot – an indication that Fe SCs do have high Tc in this sense.
Complex crystals
So far, we have assumed that cuprate superconductors and Fe SCs exist as planar crystals, with Fermi surfaces calculated from the x and y components of the momentum of electrons in the crystals. Indeed, several of the newer superconductors (including cuprates and Fe SCs, but also cobaltate, hafnium and zirconium compounds) tend to have layered crystal structures. In fact, there have been some general theoretical suggestions (from Philippe Monthoux and Ryotaro Arita with their respective collaborators) that layered systems give rise to higher Tc than ordinary materials for superconductivity that arises from electron–electron repulsion.
4 Chemical diversity in doping
This phase diagram of materials based on the superconductor BaFe2As2 illustrates how the superconducting regions (cross-hatched) emerge from the material’s various chemical make-up. The purple region shows variations made by replacing some of the iron with cobalt (electron doping), with x indicating the amount of cobalt present. The green region shows how replacing some barium atoms with potassium (hole doping) affects Tc. Finally, the orange region indicates how Tc can be altered by isovalent substitution, in which arsenic atoms are replaced with phosphorus. Experimental Tc is shown with red dots, where different superconducting regions may have different nodal structure in the pairing. The antiferromagnetic transition temperature, TN, is shown by blue dots.
For Fe SCs, though, there is the additional complication that they come in different “flavours”, with the different crystal structures we described earlier, and the type of electron pair that is formed depends on their chemical composition. Figure 4 shows that modifying “122” compounds with hole doping, electron doping or isovalent substitution (meaning arsenic atoms have been replaced with another element in the group) produces a variety of phases, including “nodeless” (each pocket in the Fermi surface is fully gapped) and “nodal” pairing (sign changes occur within a Fermi surface). Both theorists and experimentalists are trying to understand such changes in terms of the intricate Fermi surfaces arising from multi-orbital physics. The correlation of Tc with the iron-pnictogen bond angle and height has also been interpreted in such terms. Not only is more than one iron orbital relevant, but the way in which these orbitals are involved can also fluctuate in time and space, and the crystal structure itself slightly changes as we cool the sample. The effects of these phenomena on the physical properties of Fe SCs, for example a material-dependent realization of s++-wave pairing where the pockets have the same sign in the BCS gap, are now being actively examined.
One recent breakthrough occurred when HH and co-workers made an iron-based superconductor with a lot of hydrogen doping. This modification produced a “double-dome” pattern in the behaviour of Tc, which Kuroki and colleagues think is due to subtle changes in the electronic structure in the multi-orbital system.
Another intriguing possibility, again related to the multi-orbital character of Fe SCs, is that they could be used as a “playground” for investigating violations of time-reversal symmetry. Normally, transitions between different phases of matter look the same if we take a “video” of them happening and play it back in reverse (although there are important exceptions in, for example, magnets, where the aligned spins will point in the opposite direction when time is reversed). Superconductors usually obey this time-reversal symmetry, but in principle, time-reversal broken versions are possible. So far, this time-reversal broken superconductivity is rare, occurring in, for example, a compound of ruthenium (Sr2RuO4), but the subtle balance and competition arising from multiple orbits and pocketed Fermi surfaces in Fe SCs may suggest that it could also be achieved there.
As for Tc, its maximum value in Fe SCs is still only moderate (< 77 K) when compared with the cuprates. A discovery of new materials with higher Tc would be highly desirable both for fundamental theory and for applications (see box “Putting iron-based superconductors to work”). A distinct feature of the iron-based superconductors, though, is the large diversity in their parent materials (they typically contain two other elements in addition to iron), which gives materials scientists a lot to play around with. Fe SCs also seem to respond very sensitively to modifications caused by other factors such as pressure and the substrate on which they are made. For instance, the “11” compound FeSe has the simplest crystal structure in the iron-based families, and a relatively low (8 K) Tc at atmospheric pressure, but this is drastically enhanced to 37 K under a high pressure of 9 GPa. Another avenue for increasing Tc is to use epitaxy: when FeSe is grown as an atomic monolayer deposited on SrTiO3:Nd substrates, studies using scanning tunnelling spectroscopy have found that it has an energy gap of about 20 meV. If this gap originates from superconductivity, then its Tc would lie above 77 K, although this will have to be confirmed by measurement of the Meissner effect – the expulsion of magnetic field that is a sure indication of superconductivity.
Putting iron-based superconductors to work
Thinking ahead Hideo Hosono, Yoichi Kamihara, Hideo Aoki and Kazuhiko Kuroki, shortly after their discovery of iron-based superconductors in 2008. (Courtesy: Tokyo Institute of Technology)
In the seven years that have passed since their discovery, some applications of iron-based superconductors (Fe SCs) have already been demonstrated. Their fabrication (via the deposition of thin films on top of a crystal substrate) has been extensively studied, especially for BaFe2As2, a material with Tc=25K. Researchers have also succeeded in using Fe SCs to fabricate Josephson junctions (two superconductors coupled by a weak link, such as very thin non-superconducting material) and superconducting quantum interference devices (SQUIDs).
Perhaps the most important application of superconductivity, in general, is the generation of strong magnetic fields with superconducting wires. In this application, it is important that the supercurrent should not depend much on the direction of current flow. In addition, the superconducting material must be able to tolerate very intense currents and magnetic fields; superconductivity is known to be destroyed by strong currents above a critical current density, Jc, and by magnetic fields above an upper critical field, Hc2. It is therefore imperative to maximize their values as well, not just Tc on its own.
Early studies found that Fe SCs have a high Hc2, and also that their crystal structure in the superconducting phase is favourable for wire applications. More specifically, their crystals look the same after being rotated by 90° (tetragonal symmetry), so the crystals that make up a wire must be aligned along just two axes. As for the maximum critical current density, this, for thin films, has now reached Jc = 0.5 × 106 A/cm2 at 4 K and magnetic field of 10 T for systems with an improved crystal growth technique. Jc has recently been increased in BaFe2(As1–xPx)2 (max Tc = 31 K) to 1.1 × 106 A/cm2 (or 7 × 106 at 4 K in zero magnetic field).
If Fe SCs are to be used as wires, we need to ensure that Jc is not easily affected by any misalignments between adjacent crystallites, which can be characterized by the critical grain-boundary angle beyond which Jc starts to drop rapidly. The critical angle has been determined with epitaxial thin films deposited on twinned single crystalline substrates that are artificially joined with various titling angles, and it turns out to be 9–10° – almost twice that of the cuprates. This finding is encouraging for wire fabrication, because superconducting wires have many polycrystals, where tolerance of large tilting angles between neighbouring crystallites makes it easier to fabricate wires with higher Jc.
The maximum Jc has evolved in iron-based superconducting wires fabricated by the conventional “powder-in-tube” (PIT) method, in which a metal pipe filled with superconducting powder is shaped into a wire mechanically. Intense efforts by research groups in the US, Japan and China during the last two years have brought the maximum value above the level required for practical applications, which is 105 A/cm2 at 4 K and 10 T. The “122” compounds, in particular, occupy a unique position in applicable regions in the temperature-magnetic field diagram; the fact that they (like conventional metallic superconductors, but unlike the cuprates) can be fabricated by the PIT method gives them an advantage as well. These compounds have supercurrents that depend little on the direction of the current, which also favours applications. We can thus expect high-field applications below 30 K. All of these achievements have been made in flat wires, so one of the next technical hurdles will be to realize them in round wires.
Outlook
In 2011 Physics World published a special issue reviewing the first 100 years of superconductivity. Iron-based superconductors have been around for only a small part of this long history, and there is still a lot to be done. The challenge for both theorists and experimentalists now is to make the best of the versatility of these multi-orbital materials, with all the many “actors” (spin, charge, orbital and lattice degrees of freedom) that influence their properties. Applications are coming into sight, although some challenges will have to be overcome before these materials can prove their worth outside the laboratory; above all, their Tc needs to be higher.
In a broader context, Fe SCs are useful for the growing field of “functional materials design”. We can, for instance, ask ourselves if it is possible to replace iron with other elements. We can explore how superconductors made from transition-metal compounds compare to light-element ones such as carbon-based superconductors. We can also try to apply the hydrogen doping mentioned above to entirely different classes of materials. Developments in iron-based superconductors may even give us new ways to exploit the feedback between solid-state systems and cold atoms trapped in optical lattices, which are being established as a “quantum simulator” of the former. The next few years of the “Iron Age” should reveal the answers.
“Other artists use oil paints or watercolour as media,” said Eric Heller, a professor of chemistry and physics at Harvard University who creates digital art based on his research. “I use quantum phenomena like resonance and branch flow.” He pointed to Random Sphere I – a painting of what looked like a golden globe covered by a dense tangle of darker lines, resembling the turbulent surface of the Sun. “Here my medium is a random wave.”
Heller and I were at the opening in December of “Art and the quantum moment” – a show held in the art gallery at the Simons Center for Geometry and Physics at Stony Brook University in New York. Curated by Lorraine Walsh, it was inspired by a book I co-authored with Alfred Scharff Goldhaber called The Quantum Moment: How Planck, Bohr, Einstein, and Heisenberg Taught Us to Love Uncertainty (Norton 2014). The book describes how and why the imagery and language of quantum mechanics went mainstream and came to influence art and culture.
Although Heller and the other two artists in the show – Frédérique Swist and Jacqueline Thomas – are not mentioned in the book, they each draw inspiration from quantum mechanics in different ways.
Eric Heller
Heller first got interested in photography when he was a graduate student at Harvard (1968–1973). He then started to paint as a professor at the University of California, Los Angeles, before mastering computer graphics while on sabbatical at Los Alamos National Laboratory in 1981. Heller’s artistic activity really took off, however, when he moved to the University of Washington in 1984 and began to graphically reimagine some of the phenomena he was examining (see www.ericjhellergallery.com).
“I was studying branch flow,” he told me, “or what happens when you launch a series of electrons from a single point at slightly different angles and let them flow over the equivalent of a bumpy floor.” Heller recalled that he started to play with the patterns graphically. He pointed to Transport XIII, which shows a dense set of differently coloured electron paths branching out from a point, juxtaposed with a random quantum wave on the surface of a sphere. The eerie result looks like a silver moon rising over a tangle of multicoloured threads.
We walked past Heller’s eight other works in the show. These, too, are graphical reimaginings of quantum phenomena he has studied. “I choose an image that I’ve found while playing around with the media,” he explained, “then finish it in Photoshop without making significant structural transformations to the original images.” However, Heller admits to being quite selective. “I’m very choosy. Some of these images would not work for me at all if the colour changed by 1%.” All his images nevertheless have science behind them. “I’m not a mathematical tourist,” he insists.
When I asked him what that meant, Heller drew a comparison. “It’s the difference,” he said, “between a tourist with a good camera taking a picture of some pretty piece of landscape and hanging it on the wall – and a geologist who is an expert in the landscape who recognizes that a particular formation illustrates a fundamental part of the region’s geology and is also pretty, taking a picture of that, and hanging it on the wall.”
Frédérique Swist
Frédérique Swist, senior designer at IOP Publishing, which publishes Physics World, contributed two works to the exhibit, and also came for the opening. Her work (fredswist.co.uk/gallery.html) often illustrates properties of wave interference, resonance, oscillations, and excitation functions. Swist says she often begins with technical graphs, then – unlike Heller – significantly transposes and reconstructs them.
One of her works on display was Excitable Waves (2010), which reinterprets the distribution of excitation functions in a study of biological cells adhering to physical surfaces. It was inspired by a figure in a paper published in the journal Physical Biology in 2009. “As I worked on it and added different lines and levels of colour,” Swist told me, “it acquired more layering and depth, and grew to become an image in its own right.”
Good Vibrations – Swist’s other piece in the show – was inspired by a project exploring the theme of affirmation and positivity that she was asked to join. In it Swist drew on her visual vocabulary of graphs and diagrams to produce a startling set of optical effects that she called a “visual rhythm”. Although depicted on a flat plane, the forms create a 3D effect of several superimposed planes that seem to vibrate, even expand and contract.
Jacqueline Thomas
A plinth in the gallery displayed two handmade, limited-edition books by British artist-designer Jacqueline Thomas from the Stanley Picker Gallery at Kingston University (www.jacquelinethomasbooks.co.uk). Equations (2005) and Constants (2006) consist of hand-sewn and hand-bound pages on which Thomas has created “digital collages”, fitting graphics with equations and spelled-out constants together in a puzzle-like fashion until the result looked right to her.
“I am fascinated by the knowledge that complex explanations can be simplified into a series of numbers and symbols,” Thomas told me. “As someone who recognizes the significance of the equations and constants, but without any real understanding, I can only respond to their beauty in visual terms. However, they were carefully selected by someone who understands and refers to the ‘beauty of mathematics’ – my astrophysicist daughter.”
The critical point
Classical mechanics has long had an impact on graphic arts, which persists to this day in the form of maps of self-similar systems associated with a relatively recent branch of mechanics, chaos theory. It is not surprising that the weirdness of quantum mechanics is also influencing graphic artists – be it Heller’s reimaginings of quantum phenomena, Swist’s transformations of representations of the incredibly precise and reproducible patterns, or Thomas’s collages based on the imagery of the language in which quantum language is expressed.
Comparing the (a) typical crystal structure, (b) Fermi surface and (c) superconducting gap in momentum space of the iron-based (left) and cuprate (right) superconductors. 
