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Tandem solar cells break new record – Physics World




tandem solar cell
Schematic structure of the tandem solar cell stack in 3D. Credit: Eike Koehnen/HZB

Solar cells made from a combination of silicon and a complex perovskite have reached a new milestone for efficiency. The new tandem devices, made by Steve Albrecht and colleagues at the Helmholtz-Zentrum Berlin, Germany, have a photovoltaic conversion efficiency (PCE) of 29.15%, beating out the previous best reported value of 26.2%. They also retain 95% of their initial efficiency even after 300 hours of operation and have an open-circuit voltage as high as 1.92 V.

Solar cells containing two photoactive semiconducting materials with different but complementary electronic band gaps can reach much higher PCEs when used in a tandem configuration than either material on its own. Perovskites, which have the chemical formula ABX3 (where A is typically caesium, methylammonium or formamidinium; B is lead or tin; and X is iodine, bromine or chlorine), are one of the most promising thin-film solar-cell materials around because they are efficient at converting the visible part of the solar spectrum into electrical energy. Since silicon is an efficient absorber of infrared light, combining silicon with a perovskite helps to make the most of the Sun’s output.

“Perfect bed” for perovskite

Working with Vytautas Getautis and his team at the Kaunas Technical University in Lithuania, Albrecht and colleagues constructed their tandem solar cell by sandwiching a self-assembled monolayer (SAM) of a novel carbazole-based molecule between a complex perovskite with a 1.68 eV band gap and an indium tin oxide electrode connected to the silicon. Electrical charge carriers (electrons and holes) can diffuse through perovskites quickly and over long lengths, and adding the SAM layer facilitates the flow of electrons and holes even further. “We first prepared the perfect bed, so to speak, on which the perovskite lays on,” explains Amran Al-Ashouri, a member of Albrecht’s team.

To understand the various processes at play at the interface of the perovskite and the SAM, the researchers studied the interface using a combination of transient photoluminescence spectroscopy, computational modelling, electrical characterization and time-resolved terahertz photoconductivity measurements. The information gleaned from these and other techniques enabled them to optimize the device’s so-called fill factor – a key parameter for photovoltaic devices, and one where perovskite-based solar cells have long fallen short of better-established solar cell materials.

Accelerating hole transport

In Albrecht and colleagues’ experiments, the fill factor depends on how many charge carriers are “lost” on their way out of the SAM-perovskite interface. These losses occur due to a process known as nonradiative recombination, in which excited electrons and holes recombine without emitting light – an unwanted interaction that lowers the efficiency of power conversion.

In the new tandem device, the electrons flow in the direction of incoming sunlight through the SAM, while the holes move in the opposite direction through the SAM into the electrode. The researchers observed, however, that the speed at which holes are extracted is much lower than the corresponding speed for electrons – something that would normally limit the fill factor. According to Al-Ashouri, the new SAM solves this problem by considerably accelerating hole transport, which improves the fill factor and makes the perovskite cell more efficient.

Members of the team, which also includes researchers from the universities of Potsdam in Germany, Ljubljana in Slovenia and Sheffield in the UK as well as the Physikalisch-Technische Bundesanstalt (PTB), HTW Berlin and the Technische Universität Berlin, say that the maximum PCE possible for their design — 32.4% — is now “within reach”. “To this end, we plan to further reduce resistive losses in the tandem solar cell to explore the full PCE potential well above 30%,” team member Eike Köhnen tells Physics World.

The research is detailed in Science.



‘Unicorn’ Discovery Points to a New Population of Black Holes




Almost a decade ago, Feryal Özel and her colleagues noticed something odd. While a variety of possible black holes had been found in our galaxy, none appeared to fall below a certain size. “There seemed to be a dearth of black holes below 5 solar masses,” she said. “Statistically, this was very significant.”

Since Özel, an astrophysicist at the University of Arizona, published a paper on the problem in 2010, this so-called mass gap has gone unexplained. Even after the LIGO and Virgo gravitational wave detectors started to identify dozens of hidden black holes — including a few surprises — the mass gap appeared to hold firm.

In time, astrophysicists such as Özel began to wonder: Are small black holes just hard to find, or might they not exist at all? “It’s important to establish observationally whether this gap is real, or whether it’s an observational artifact,” said Vicky Kalogera, an astrophysicist at Northwestern University and a leading member of the LIGO team.

Recent discoveries are beginning to suggest the latter might be the case. In the past two years, researchers have found several possible black holes in the mass gap. Then, earlier this month, astronomers presented evidence of what might be our best candidate yet — a 2.9-solar-mass object dubbed “the unicorn.”

Before LIGO, astronomers found black holes mostly by searching for the X-rays they produce as they suck in matter from a nearby star. They could also detect the gravitational effect a black hole would have on another star in a binary system. The unicorn researchers used this latter method, focusing on a system called V723 Monoceros, located about 1,000 light-years away. They studied the motion of a red giant star with a variety of telescopes, including the European Space Agency’s Gaia satellite, which is mapping the position of billions of stars in our galaxy, and NASA’s exoplanet-hunting Transiting Exoplanet Survey Satellite (TESS).

The researchers concluded that the red giant appears to be dancing with an unseen partner. “The simplest explanation for the dark companion is a single compact object, most likely a black hole, in the ‘mass gap,’” the team wrote.

The discovery, if confirmed, would help illuminate the fine distinction that nature makes at the end of a massive star’s life. When a giant star exhausts its fuel, the star’s mass flows inward and its core collapses. If the incoming mass can explode and overcome the star’s gravitational force, it bursts into a supernova. But if not — if there’s just too much mass — the star collapses in on itself and forms a black hole.

“It’s a race between the explosion happening and black hole formation,” said Todd Thompson, a theoretical astrophysicist at Ohio State University and a co-author of the recent paper. “This race has to be won within about a second. If it doesn’t explode in that one second, then it forms a black hole. If it does explode, it leaves behind a neutron star.”

Exactly what determines whether a star explodes as a supernova or collapses into a black hole isn’t clear. “The actual physics of the supernova explosion is a huge unknown,” said Thompson. The black hole mass gap “could be a vital clue to that process.”

There have been a few tentative discoveries in the mass gap so far. Benjamin Giesers from the University of Göttingen and colleagues discovered a possible 4.4-solar-mass black hole in 2018, while Thompson and his colleagues found a 3.3-solar-mass candidate in 2019.

Then last year, scientists from LIGO announced the detection of an object 2.6 times the mass of our sun, a very tantalizing candidate with a mass comfortably in the mass gap. “The best case for a mass-gap black hole is from LIGO,” said Thompson.

Yet at these lower masses, it’s hard to tell the difference between a black hole and a neutron star, since the latter can bulk up to a theoretical maximum of 3 solar masses. And depending on the conditions, neutron stars can appear dark as well. “If a neutron star is a pulsar with a beam pointed at you, it does some very obvious things,” said Tom Maccarone, an expert in black holes and neutron stars at Texas Tech University. “But if it’s not, it can be very difficult to separate” from a black hole.

As such, black hole discoveries such as the recent one from LIGO are still unconfirmed, as is the unicorn. “It looks plausible,” said Özel. “I think their methods are sound and the analysis is careful. There are still a couple of other possibilities as far as what it could be, but the conclusion that they come to — that it is most likely a single dark object with a mass of 2.9 solar masses — seems sound to me.”

Not everyone is so sure. For one thing, it’s possible the system is not a binary but a triple system, with two smaller objects accounting for the missing mass. Maccarone also said that if the unicorn is a black hole, it should be pulling matter away from its companion star and creating X-rays. “The X-ray luminosity is so faint for the black hole scenario,” he said.

There is also uncertainty about the mass of the object itself. While the best estimate is 2.9 solar masses, the authors say it could weigh as little as 2.6 and as much as 3.6 solar masses. “This range is too broad for us to be certain this is [not] a neutron star,” said Kalogera. “And there is nothing else in the observations that allows us to distinguish between a neutron star and a black hole.”

If this discovery turns out not to be a black hole — and especially if the other candidates don’t hold up to scrutiny either — then perhaps black holes simply do not form below 5 solar masses. Such a revelation would carry significant implications for our understanding of supernova physics. “If you really have a gap there, it suggests a very rapid explosion mechanism,” said Maccarone. “We don’t understand what drives supernova explosions well enough to have a strong theoretical bias for what to expect.”

But if the unicorn really is a black hole, it could be one of many in this gap waiting to be discovered and studied. “That’s what’s exciting about this paper,” says Özel. “If we come to a point where we know more than one or two of these objects, then we can understand what types of processes lead to these smaller-mass black holes.”


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Learning physics from migrating bacteria




Fruiting bodies
Droplet-like fruiting bodies of the bacterium M. xanthus. Each fruiting body contains hundreds of thousands of bacterial cells and is tens to hundreds of times taller than a single cell. (Courtesy: Cassidy Yang)

Myxococcus xanthus is a rod-shaped soil bacterium with the ability to move on surfaces. Under starvation conditions, individually migrating bacteria switch their motile behaviour and cooperate to form dome-shaped multicellular structures known as fruiting bodies. The physics behind the creation of these multilayer structures, however, is not well-understood.

Intrigued by the densely packed and aligned structure of such M. xanthus colonies, a group of researchers at Princeton University in the US investigated the physics underlying fruiting body formation. Their study, published in Nature Physics, reveals that the collective dynamics of migrating bacterial colonies resembles the physics underlying active nematic liquid crystals.

Topological defects in bacterial colonies

To record a wide range of motility-driven collective dynamics of M. xanthus colonies, Katherine Copenhagen at the Lewis-Sigler Institute for Integrative Genomics at Princeton University imaged the colonies using a laser scanning confocal microscope. Copenhagen and group leader Joshua Shaevitz placed the colonies on an agar substrate in the presence of nutrients and, without labelling the cells, used the light reflected from the colony’s surface to measure cell alignment.

Since nutrients were present, no fruiting bodies appeared. However, the researchers observed that new cell layers and holes spontaneously appeared and disappeared. These layers and holes appeared preferentially at points known as topological defects – singularities in the cell orientation field where cells oriented in all directions meet.

These observations motivated the researchers to study this non-equilibrium collective behaviour using the physical framework of active nematic liquid crystals. Active nematics are a class of material made up of elongated particles that align with each other and are able to move on their own – precisely like the bacteria.

To dig into the theoretical physics aspects of active nematics, Ricard Alert at the Princeton Center for Theoretical Science worked with Ned Wingreen to develop a theory for the bacterial colony. Impressively, the experimental data and the theoretical predictions went hand-in-hand.

The study authors

“A moment that I remember quite vividly,” Alert says, “is watching these videos at the very beginning of this project and starting to realize, wait, do layers form exactly where the topological defects are? Could it be true?” This motivated him to explain the experimental observations via analytical calculations.

“The orientation of rod-shaped particles induced an increased friction from the front to the tail of the defect, leading to cell accumulation at the front and eventually cell extrusion in the third dimension”, explain Marc-Antoine Fardin and Benoît Ladoux from CNRS, in their news and views article for this study.

The researchers propose that cell motility and mechanical interactions between the cells are two key drivers of the formation of multilayered structures. However, since these studies were performed while nutrients were available, future studies under starvation-induced conditions will be important to fully understand the role and characteristics of fruiting bodies.


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Topology 101: The Hole Truth




If you’re looking to pick a fight, simply ask your friends, “Is Pluto a planet?” Or “Is a hotdog a sandwich?” Or “How many holes does a straw have?” The first two questions will have them arguing yay or nay, while the third yields claims of two, one and even zero.

These questions all hinge on definitions. What is the precise definition of a planet? A sandwich? A hole? We will leave the first two for your friends to argue about. The third, however, can be viewed through a mathematical lens. How have mathematicians — particularly topologists, who study spatial relationships — thought about holes?

In everyday language, we use “hole” in a variety of nonequivalent ways. One is as a cavity, like a pit dug in the ground. Another is as an opening or aperture in an object, like a tunnel through a mountain or the punches in three-ring binder paper. Yet another is as a completely enclosed space, such as an air pocket in Swiss cheese. A topologist would say that all but the first example are holes. But to understand why – and why mathematicians even care about holes in the first place — we have to travel through the history of topology, starting with how it differs from its close kin, geometry.

In geometry, shapes like circles and polyhedra are rigid objects; the tools of the trade are lengths, angles and areas. But in topology, shapes are flexible things, as if made from rubber. A topologist is free to stretch and twist a shape. Even cutting and gluing are allowed, as long as the cut is precisely reglued. A sphere and a cube are distinct geometric objects, but to a topologist, they’re indistinguishable. If you want a mathematical justification that a T-shirt and a pair of pants are different, you should turn to a topologist, not a geometer. The explanation: They have different numbers of holes.

Leonhard Euler kicked off the topological investigation of shapes in the 18th century. You might think that by then mathematicians knew almost all there was to know about polyhedra. But in 1750, Euler discovered what I consider one of the all-time great theorems: If a polyhedron has F polygonal faces, E edges and V vertices, then V E + F = 2. For example, a soccer ball has 20 white hexagonal and 12 black pentagonal patches for a total of 32 faces, as well as 90 edges and 60 vertices. And, indeed, 60 – 90 + 32 = 2. This elementary observation has deep connections to many areas of mathematics and yet is simple enough to be taught to kindergartners. But it eluded centuries of geometers like Euclid, Archimedes and Kepler because the result does not depend on geometry. It depends only on the shape itself: It is topological.

Euler implicitly assumed his polyhedra were convex, meaning a line segment joining any two points stayed completely within the polyhedron. Before long, scholars found nonconvex exceptions to Euler’s formula. For instance, in 1813 the Swiss mathematician Simon Lhuilier recognized that if we punch a hole in a polyhedron to make it more donut-shaped, changing its topology, then VE + F = 0.

Interestingly, while Euler and Lhuilier imagined their polyhedra as solid, Euler’s formula is computed using only zero-dimensional vertices, one-dimensional edges and two-dimensional faces. So Euler’s number (VE + F) actually derives from the two-dimensional surface of the polyhedron. Today, we would imagine these shapes as hollow shells.

Moreover, all that matters is the topology of the object. If we make a polyhedron out of clay, mark the edges with a Sharpie, and roll it into a ball, the faces and edges become curved but their number doesn’t change. So for any shape that is topologically a sphere, its Euler number is 2; for a donut-like torus, it’s 0; for a flat disk it’s 1; and so on. Each surface has its own Euler number. This topological understanding of Euler’s formula — in which the shapes were rubber-like and not rigid — was first presented in an article by Johann Listing in 1861. Although largely forgotten today, Listing is also notable for writing about the Möbius band four years before August Möbius, and for coining the very term topologie.

Around the same time, Bernhard Riemann was studying surfaces that arose in his study of complex numbers. He observed that one way of counting holes was by seeing how many times the object could be cut without producing two pieces. For a surface with boundary, such as a straw with its two boundary circles, each cut must begin and end on a boundary. So, according to Riemann, because a straw can be cut only once — from end to end — it has exactly one hole. If the surface does not have a boundary, like a torus, the first cut must begin and end at the same point. A hollow torus can be cut twice — once around the tube and then along the resulting cylinder — so by this definition, it has two holes.

Henri Poincaré was the next to build on, and greatly expand, the study of topology, when he published the groundbreaking 123-page article “Analysis Situs” in 1895. In it and its five sequels, he planted numerous topological seeds that would grow, blossom and bear fruit for decades to come. Notable among these was the concept of homology, which Poincaré introduced to generalize Riemann’s ideas to higher dimensions. Through homology, Poincaré aimed to capture everything from Riemann’s one-dimensional circle-like holes in a straw or binder paper, to the two-dimensional cavity-like holes inside Swiss cheese, and beyond to higher dimensions. The number of these holes — one for each dimension — became known as the Betti numbers of the object in honor of Enrico Betti, a friend of Riemann’s who had attempted similar work.

The modern definition of homology is quite involved, but it is roughly a means of associating to each shape a certain mathematical object. From this object we can extract simpler information about the shape, like its Betti numbers or its Euler number.

To get a sense of what homology and Betti numbers are, let’s focus on dimension one. We’ll start by looking at loops on a surface. The rules are simple: The loops can slip and slide around, and can even cross themselves, but they cannot leave the surface. On some surfaces, like a circular disk or a sphere, any loop can shrink down to a single point. Such spaces have trivial homology. But other surfaces, like a straw or a torus, have loops that wrap around their holes. These have nontrivial homology.

The torus shows us how to visualize Betti numbers. We can produce infinitely many nontrivial loops on one, and they can wind, double back and wrap around multiple times before ending at their starting point. But rather than producing a chaotic mess, these loops possess an elegant mathematical structure. Let’s call a loop that goes through the central hole and around the tube once “a.” That now serves as the basis for more loops. Since a loop can go around the tube once, twice or any number of times, and direction matters, we can represent those loops as a, 2a, –a, and so on. Not every loop is a multiple of a, however, such as the loop going around the central hole along the tube’s long circumference, which we can call “b.” At this point, though, there are no more unique trips: Any loop on the torus can be deformed to follow loops a and b some integer number of times. That there are two one-dimensional loops from which all others can be built means that the Betti number of the torus in dimension one is 2, the same as the number of Riemann’s cuts.

If loop c is equivalent to loop a combined with loop b, we write c = a + b. This expression is not just a notational convenience. It’s possible to make this arithmetic — the addition and subtractions of loops — rigorous. In mathematical lingo, a set that allows addition and subtraction is called a group. So on the torus, for example, the one-dimensional homology group consists of expressions such as 7a + 5b, 2a – 3b, and so on.

Fittingly, the group structure of homology was discovered in the 1920s by Emmy Noether, a pioneer of the study of groups and other algebraic structures. Thanks to Noether’s observation, mathematicians can now harness the power, structure and theorems of algebra to understand topology. For instance, we can say with mathematical certainty that a straw, a T-shirt and a pair of pants are all topologically different objects because their homology groups are different. In particular, they have a different number of holes.

So, finally, how do topologists count holes? Using the Betti numbers. The zeroth Betti number, b0, is sort of a special case. It simply counts the number of objects. So for a single connected shape, b0 = 1. As we just saw, the first Betti number, b1, is the number of circular holes in a shape — like the circle around the cylindrical straw, the three holes in binder paper and the two circular directions of the torus. And Poincaré showed us how to compute homology, and thus the associated Betti numbers, in higher dimensions as well: The second Betti number, b2, is the number of cavities — like those inside a sphere, a torus and Swiss cheese. More generally, bn counts the number of n-dimensional holes.

Remarkably, Poincaré’s homology brings us full circle back to Euler. Just as Euler’s number for a surface can be computed with vertices, edges and faces, it can also be computed with its Betti numbers: b0 b1 + b2. The torus, for instance, is connected, so b0 = 1; it has b1 = 2, as we’ve seen; and, because it has one internal cavity, b2 = 1. Just as Lhuilier noted, the Euler number of the torus is 1 – 2 + 1 = 0.

Although mathematicians have had a basic understanding of homology for almost a century, algebraic topology continues to be an active research area further binding together algebra and topology. Researchers have also been branching out in other directions, developing the theory and algorithms necessary to compute the homology of shapes that are represented digitally, building tools to identify the underlying shape of large data sets (which often reside in high-dimensional spaces), and so on.

Yet others have been applying these theoretical tools to real-world applications. Imagine, for example, a scattered collection of small, low-cost sensors that detect something — movement, fire, gaseous emissions — within some fixed coverage radius. The sensors don’t know their locations, but they do know which other sensors are nearby. In 2007 Vin de Silva and Robert Ghrist showed how to use homology to detect holes in the sensors’ coverage, based on just this crude information. In a more recent paper, Michelle Feng and Mason Porter used a new technique called persistent homology to detect political islands — geographical holes in one candidate’s support that serve as spots of support for the other candidate — in California during the 2016 presidential election.

Thus, as with so many areas of pure mathematics that began as mere theoretical musings, topology has proved its real-world worth, and not just for settling the question of how many holes a straw has.


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Hollow-core fibre boosts optical gyroscope performance




Fibre-optic gyroscopes (FOGs) rely on a pair of laser beams travelling in opposite directions around the same fibre-optic coil. If the reference frame of the beams is not inertial – that is, if the gyroscope is rotating – the beam travelling counter to the direction of the rotation will experience a slightly shorter path. This path-shortening phenomenon is known as the Sagnac effect, and when the two light beams are made to interfere, their interference signal can be used to calculate the difference in path length. This, in turn, shows how the gyroscope (or the vehicle upon which it is mounted) changed its orientation.

Recirculating light

The sensitivity of FOGs can be enhanced by increasing the distance the light travels, for example by sending the light down a longer fibre-optic cable. Resonator fibre optic gyroscopes (RFOGs) exploit this principle by connecting the ends of the optical fibre to form an optical resonator. Because most of the light takes multiple trips around the fibre coil, RFOGs are more sensitive than simple FOGs, and any rotation-induced difference in path lengths manifests itself as a difference in the resonance frequencies in each direction.

Certain nonlinear optical effects can, however, degrade an RFOG’s performance. Identifying optical fibres that are immune to such effects has proved challenging, says project leader Glen Sanders, adding that he and his team at Honeywell International had previously examined whether hollow-core fibres that confine light in a central or gas-filled void might overcome the problem.

Even fewer nonlinear effects

In the latest study, which appears in Optics Letters, researchers co-led by Austin Taranta of the University of Southampton in the UK employed a type of hollow-core fibre known as a nodeless anti-resonant fibre (NANF). This type of fibre shows even fewer nonlinear effects than other hollow-core fibres, and it also has a low optical attenuation, which improves the quality of the resonator because the intensity of light remains steady over a longer propagation distance. Indeed, NANFs have the lowest optical loss of any hollow fibre – and for many parts of the electromagnetic spectrum, the lowest loss of any optical fibre, Taranta says.

Sanders adds that using a NANF eliminates optical errors caused by effects such as backscattering, polarization coupling and modal impurities, all of which can produce errors or extra noise in the gyroscope. “Eliminating these effects allows the light to travel along a single path through the fibre, a prerequisite for RFOGs,” he explains.

The Honeywell researchers tested their new gyroscope by mounting it on a stable static pier, which eliminates all rotation effects apart from the Earth’s rotation. This allowed them to determine that the “bias stability” for the instrument is just 0.05 degrees per hour, for observation times between 1-10 hours. This is 500 times better than previous measurements on hollow core fibre-based RFOGs for periods of longer than an hour, and close to the level required for civil aircraft navigation, the researchers say.

The team now plans to build a prototype gyroscope with a more compact and stable configuration that employs the latest generation of NANFs.


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