New production method for flexible, durable anodes with high capacity-to-weight

A team of researchers from Humboldt Universität zu Berlin, the Leibniz-Institut für Polymerforschung Dresden (IPF) e. V., and the Karlsruhe Institute of Technology (KIT) have made an anode with superior performance for portable battery applications, close to limits of theoretical capacity. Uniquely, the obtained anodes are flexible without surface reconstruction or crack formation, and they survive heat shocks without performance-loss.

Conventional batteries break down when subjected to mechanical and thermal stress. As a necessity, they need to be situated in stiff, rigid sections of nominally “foldable” electronics and away from sources of heat. The fundamental limitation of the conventional production methods is that the free motion of binders and additives used for battery assembly will lead, over time, to a detrimental loss of the desired electrochemical bias, and finally to a dead battery. To overcome this limitation, the team of Prof. Michael J. Bojdys, the team leader at Humboldt Universität zu Berlin, had the idea to replace conventional binders and additives with a semi-conducting porous organic polymer that (i) adheres to the current collector and grows around the active material, and (ii) enables transport of electrolyte and charge-carriers.

Prof. Bojdys says “Batteries work because we carefully build a chemical bias from small particles. You see this represented in the plus-pole and minus-pole on the battery. Now, what happens if you start shaking or heating such an ordered system? Well, you destroy the chemical bias, and the battery is dead! The way how we build conventional batteries is comparable to putting all your shopping loosely into your car trunk – by the time you get home, everything is jumbled up. Now, if you want to keep your shopping ordered, you obviously put it into bags! This is the role that our semi-conducting porous polymer plays in our electrodes. The polymer replaces all classic battery additives, and it leads to fantastic performance.”

Based on this technology Dr. Goshtasp Cheraghian and Prof. Dr. Michael J. Bojdys seek to commercialize their electrodes and ink-formulations as part of the INAM AdMaLab 2022 Incubator Program.

The article appeared online as:
One‐pot synthesis of high‐capacity silicon anodes via on‐copper growth of a semiconducting, porous polymer
J. Huang, A. Martin, A. Urbanski, R. Kulkarni, P. Amsalem, M. Exner, G. Li, J. Müller, D. Burmeister, N. Koch, T. Brezesinski, N. Pinna, P. Uhlmann, and M.J. Bojdys
Natural Sciences, published online (2022) ^OPENACCESS
DOI: 10.1002/ntls.20210105

 

FAIR research data in materials sciences

The FAIRmat consortium led by Humboldt-Universität zu Berlin describes its concept for accessible research data in the renowned journal Nature

How the FAIRmat consortium works (Copyright: FAIRmat)

The lifestyle of our society is largely determined by the achievements of condensed matter physics, chemistry and material sciences. Touch screens, batteries, electronics or implants: Many new products in the fields of energy, environment, health, mobility and information technology are largely based on improved or even novel materials. These fields generate enormous amounts of data every day, which is a new raw material - and is therefore a gold mine in itself. However, a prerequisite for this is that these data are comprehensively characterized and made available to science.

FAIR data for shared use

The FAIRmat consortium ("FAIR Data Infrastructure for Condensed-Matter Physics and the Chemical Physics of Solids"), led by IRIS Adlershof member Prof. Claudia Draxl, aims to refine this raw material, i.e. turning data into knowledge and value. A prerequisite is a data infrastructure that makes enables scientific data to be „FAIR", i.e. findable, accessible, interoperable and re-purposable. "With a "FAIR" infrastructure, data can be easily shared and explored using data analytics and artificial intelligence methods. This approach will significantly change the way how science is done today," says Claudia Draxl.

In the journal Nature, the scientists describe how such a data infrastructure can be successfully implemented in the field of materials science. The article appears today in the "Perspectives" format, in which the journal publishes forward-looking contributions that stimulate discussion and new scientific approaches.

The FAIRmat consortium is part of the initiative “Nationale Forschungsdaten Infrastruktur” (NFDI). The project is based on the extensive experience with the world's largest data infrastructure in computational materials science, the Novel Materials Discovery (NOMAD) Laboratory, which was co-founded by Claudia Draxl and has been online since 2014. The main challenge for FAIRmat is the integration of many different experimental characterization techniques and methods of material synthesis.

FAIR data enabling new horizons for materials research
M. Scheffler, M. Aeschlimann, M. Albrecht, T. Bereau, H.-J. Bungartz, C. Felser, M. Greiner, A. Groß, C.T. Koch, K. Kremer, W.E. Nagel, M. Scheidgen, C. Wöll, and C. Draxl
Nature 604 (2022) 635
DOI: 10.1038/s41586-022-04501-x

Contact:
Prof. Dr. Claudia Draxl
Institut für Physik / IRIS Adlershof
Humboldt-Universität zu Berlin
Tel.: 030 2093-66363
E-Mail: claudia.draxlphysik.hu-berlin.de
www.fairmat-nfdi.eu

 

Bremsstrahlung of black holes and neutron stars from quantum field theory

Fig 1: Visualization of the gravitational Bremsstrahlung from the scattering of two black holes (BSc thesis O. Babayemi)

When two massive objects (black holes, neutron stars, or stars) fly past each other, the gravitational interactions not only deflect their orbits, but also produce gravitational radiation, or gravitational bremsstrahlung, analogous to electromagnetism. The resulting gravitational waves of such a scattering event were calculated at leading order in Newton's gravitational constant in the 1970s using traditional methods of general relativity in an extensive series of four papers. Bremsstrahlung events are still out of reach for the current generation of gravitational-wave detectors because the signal is non-periodic and typically less intense. Nevertheless, they are interesting targets for future searches with future terrestrial and space-based observatories.

In the Quantum Field Theory lab around IRIS Adlerhof-member Prof. Plefka, a new approach to determining these waveforms (Fig. 1) and the deflections using methods of perturbative quantum field theory was recently developed, which proves to be significantly more efficient than the traditional approaches. It is based on a hybrid quantum field theory, in which the black holes (or stars) are idealized as point particles and interact with the gravitational field. The calculation is then based on a systematic diagrammatic expansion using Feynman graphs. I.e. the methods that were originally developed for the scattering of elementary particles can now also be used in astrophysical scenarios.

With this innovative method - the "Worldline Quantum Field Theory“ approach - our understanding of this fundamental physical process was recently significantly extended resulting in a series of three publications in the Physical Review Letters. In [1], the results from the 1970s were reproduced in a far more efficient way; this only required the calculation of three Feynman graphs (Fig. 2). In [2] the waveform could be extended to the case of rotating black holes and neutron stars. In a recent publication [3], the scattering angles and deflections in momenta and rotations due to the scattering process at the next-next-leading order of the gravitational constant were determined for the first time. Elaborated techniques for calculating Feynman integrals were used here. Interestingly, the rotational degrees of freedom of the black holes are described in this new formulation with a supersymmetric world line theory [4], which was originally developed in extensions of the Standard Model of particle physics.

This research was performed in the context of the DFG Research Training Group 2575 "Rethinking Quantum Field Theory“, where innovations in quantum field theory are developed in cooperation with the Max-Planck Institute for Gravitational Physics and the Helmholtz-Centre DESY.

Fig 2: Feynman graphs to determine the waveform. The dotted lines represent the black holes, the waves represent gravitational radiation, and the lines represent fluctuations in the black hole's orbit.

Publikations:

[1]	Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff Phys. Rev. Lett. 126 (2021) 201103 arxiv: 2101.12688  OPENACCESS		[3]	Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory G. U. Jakobsen and G. Mogull erscheint in PRL arxiv: 2201.07778  OPENACCESS
[2]	Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff Phys. Rev. Lett. 128 (2022) 011101 arxiv: 2106.10256  OPENACCESS		[4]	SUSY in the sky with gravitons G. U. Jakobsen, G. Mogull, J. Plefka, and J. Steinhoff JHEP 2201 (2022) 027 arxiv: 2109.04465  OPENACCESS

Further Informationen:
Videos on Youtube (from BSc thesis of O. Babayemi)

 

Printing an electronic rainbow –
Combination of colour printing  and chemical tunability enables printed spectrometer

Researchers from Innovation Lab HySPRINT at Helmholtz-Zentrum Berlin (HZB) and Humboldt Universität zu Berlin (HU) have used an advanced inkjet printing technique to produce a large range of photodetector devices based on a hybrid perovskite semiconductor. By mixing of only three inks, the researchers were able to precisely tune the semiconductor properties during the printing process. Inkjet printing is already an established fabrication method in industry, allowing fast and cheap solution processing. Extending the inkjet capabilities from large area coating towards combinatorial material synthesis opens the door for new possibilities for the fabrication of different kind of electronic components in a single printing step.

 

a) Combinatorial printing allows precise control of the mixing of perovskite precursor inks during film fabrication.
b) This leads to a compositional halide gradient in methylammonium-based metal halide perovskites.
c) Each perovskite composition is inkjet printed onto prefabricated interdigitated ITO electrodes to produce a series of nine photodetectors.
d) The detection onset of the photodetectors measured in external quantum efficiency directly relates to the compositional gradient of the metal halide perovskite.

Wonder material metal halide perovskites
Metal halide perovskites are fascinating to researchers in academia and industry with the large range of possible applications. The fabrication of electronic components with this material is particularly appealing, because it is possible from solution, i.e. from an ink. Commercially available salts are dissolved in a solvent and then deposited on a substrate. The group around Prof. Emil List-Kratochvil, head of a joint research group at HZB and HU, focusses on building these types of devices using advanced fabrication methods such as inkjet printing. The printer spreads the ink on a substrate and, after drying, a thin semiconductor film forms. Combining multiple steps with different materials allows to produce solar cells, LEDs or photodetectors in mere minutes.

Inkjet printing is already an established technique in industry, not only for newspapers and magazines, but also for functional materials. Metal halide perovskites are specifically interesting for inkjet printing, as their properties can be tuned by their chemical make-up. Researcher at HZB have already used inkjet printing to fabricate solar cells and LEDs made from perovskites. The inkjet capabilities were further expanded in 2020, when the group of Dr. Eva Unger first used a combinatorial approach to inkjet printing, to print different perovskite compositions in search of a better solar cell material.

Combinatorial printing approach towards industrial production of electronic devices
Now, in this current work, the team around Prof. Emil List-Kratochvil found an exciting application for a large perovskite series within wavelength-selective photodetector devices. “Combinatorial inkjet printing cannot only be used to screen different compositions of materials for solar cell materials,” he explains, “but also enables us to fabricate multiple, separate devices in a single printing step.” Looking towards an industrial process, this would enable large scale production of multiple electronic devices. Combined with printed electronic circuits, the photodetectors would form a simple spectrometer: paper thin, printed on any surface, potentially flexible, without the need of a prism or grid to separate the incoming wavelengths.

Emil List-Kratochvil is Professor of Hybrid Devices at Humboldt-Universität zu Berlin, member of IRIS Adlershof and head of a Joint Lab founded in 2018 that is operated by HU together with HZB. In addition, a team jointly headed by List-Kratochvil and HZB scientist Dr. Eva Unger is working in the Helmholtz Innovation Lab HySPRINT at HZB on the development of coating and printing processes for hybrid perovskites. For a few days she is also an IRIS Adlershof-member.

Using Combinatorial Inkjet Printing for Synthesis and Deposition of Metal Halide Perovskites in Wavelength‐Selective Photodetectors
V.R.F. Schröder, F. Hermerschmidt, S. Helper, C. Rehermann, G. Ligorio, H. Näsström, E.L. Unger, and E.J.W. List-Kratochvil
Adv. Eng. Mater. (2021) 2101111 ^OPENACCESS
DOI: 10.1002/adem.202101111

 

Sparking electroluminescence in poly(triazine imide) films

A team of researchers from King’s College London, Humboldt-Universität zu Berlin, Carl von Ossietzky Universität Oldenburg, and Helmholtz-Zentrum Berlin (HZB) have investigated the synthesis, structure, optical properties of poly(triazine imide), a member of the family of graphitic carbon nitrides. Their progress on material quality and processing allowed for construction of the first single layer, organic light emitting device (OLED) with a solution-processed graphitic organic material as a metal-free emission layer.
Organic semiconductors have sparked great interest in academic and industrial circles over the last decades, because of their advantageous properties such as (i) a high absorption coefficient compared to conventionally used silicon as well as (ii) less energy intensive production, and (iii) composition from earth-abundant elements. Progress in this field of research promises new, cost- and energy-efficient technologies in consumer electronics, smart packaging, and flexible light-emitters.
Hitherto explored organic semiconductors often suffer from degradation processes and defects especially when electrochemically altered (“doped”), due to dopant drift and migration or due to oxidation when exposed to atmospheric conditions. The unique properties of poly(triazine imide) enable the research to address the issues that plague conventional organic semiconductors. Poly(triazine imide) is a very stable under heat and air. Furthermore, the graphitic morphology of poly(triazine imide) allows exfoliation of the material into thin, solution-processable layers, while at the same time reducing migration and drift of chemically bonded dopants.
“With the improved material quality, we are now able to dive deeper into the more delicate features of this material, such as the electronic structure and vibration modes. This will greatly improve our understanding of this material, as well as related materials, and help us improving OLED performance and think about future, high-value applications of poly(triazine imide).”, says David Burmeister, PhD student at IRIS Adlershof member Michael J. Bojdys.

Optimized synthesis of solution-processable crystalline poly(triazine imide) with minimized defects for OLED application
D. Burmeister, H.A. Tran, J. Müller, M. Guerrini, C. Cocchi, J. Plaickner, Z. Kochovski, E. List-Kratochvil, M. Bojdys
Angew. Chem. Int. Ed. 2021.
DOI: 10.1002/anie.202111749

 

Shaping 2D materials with small molecules

Electronic properties of 2D materials such as graphene and transition metal chalcogenides can be tailored by shaping their topography at the nanoscale. At IRIS Adlershof, Abdul Rauf and colleagues from the RabeLab together with Igor Sokolov investigated how to shape surfaces and interfaces of 2D materials with small molecules, intercalating at the interfaces between the 2D materials and a solid substrate. Particularly, they investigated wetting of interfaces between graphene and a hydrophilic substrate, mica, with two small molecules, water and ethanol. Wetting with water leads to labyrinthine structures exhibiting branch widths down to the 10 nm scale. This is explained by a process leading to an equilibrium between electrostatic repulsion of the polar molecules preferentially oriented at the interface, and the line tension between wetted and non-wetted areas. Increasing line tension or decreasing dipole density increases the branch width, causing eventually non-structured wetting layers. The method might be used to shape 2D materials to tailor their electronic properties.

  Scanning force microscopy images of graphene surfaces shaped by an intercalating molecularly thin water layer self-assembled into labyrinthine patterns (top left), and the compact wetting front of an ethanol layer (top right). The snapshots of Molecular Dynamics simulations of the interfaces filled with molecules (bottom) helped to understand the origin of the forces driving the pattern formation. 

Shaping surfaces and interfaces of 2D materials on mica with intercalating water and ethanol
A. Rauf, J. D. Cojal González, A. Balkan, N. Severin, I. M. Sokolov, and J. P. Rabe
Molecular Physics, 119:15-16, ^OPENACCESS
DOI: 10.1080/00268976.2021.1947534

 

Fishing with Light

Molecules are usually optimized for a task by trial and error. Time-consuming iterative rounds of synthesis and characterization provide detailed insight into structure-property relationships. In order to speed up this tedious process, Niklas König and Dragos Mutruc from the HechtLab have developed a clever means to generate an equilibrating mixture, a so called dynamic constitutional library, of photoswitchable molecules and used their wavelength-specific response to select the proper candidate. Thus, they could “fish” the desired switch with light in a pool of many different switches. The method should facilitate the rapid exploration of structural diversity in functional dye chemistry.
 

Accelerated Discovery of α-Cyanodiarylethene Photoswitches
N. F. König, D. Mutruc, and S. Hecht
Journal of the American Chemical Society 143 24 (2021) 9162,
DOI: 10.1021/jacs.1c03631F 

 

Lichtblick für die Quantenforschung
HU-Forschungsteam und Partner haben erstmals die Teilchenaustauschphase von Photonen direkt gemessen

Dieses Experiment liefert den direkten Beleg für ein erstaunliches Quantenphänomen, das nur bei völlig gleichartigen Quantenobjekten beobachtet wird. Damit kommt die Quantenforschung einen wichtigen Schritt voran.

Die Teilchen, denen das Forscherteam auf der Spur ist, sind schwer zu fassen. Die Physiker untersuchen die Quantenteilchen der elektromagnetischen Wellen, auch Photonen genannt, aus denen Licht besteht. Photonen lassen sich nur dann unterscheiden, wenn sie unterschiedliche Wellenlängen haben, in unterschiedlichen Richtungen schwingen oder sich an verschiedenen Punkten in Raum und Zeit befinden.

„Wenn zwei in Wellenlänge und Schwingungsrichtung ununterscheidbare Photonen aufeinandertreffen und sich wieder trennen, haben sie gewissermaßen ihre Identität verloren“, erläutert Kurt Busch. „Man stelle sich vor, wir schicken zwei Zwillinge durch zwei Türen in einen gemeinsamen Raum. Wenn Sie wieder hinaustreten, können wir nicht feststellen, ob sie dazu jeweils dieselbe Tür benutzt haben oder nicht“, ergänzt Oliver Benson, Mitglied von IRIS Adlershof. In der Quantenmechanik passiert dennoch etwas. Laut dem sogenannten Symmetrisierungspostulat gibt es zwei Kategorien von Elementarteilchen: Bosonen und Fermionen. Diese Arten von Teilchen unterscheiden sich dahingehend, was passiert, wenn man sie miteinander vertauscht.

 

Abbildung 1: Konzeptionelle Skizze des Interferometeraufbaus: a Ein verschränktes Photonenpaar (roter Strahl) wird in das Interferometer geleitet, welches zwei unterschiedliche Möglichkeiten am zentralen polarisierenden Strahlteiler (PBS) produziert, wie in b gezeigt: Entweder das Photon in Pfad 1 wird transmittiert und das Photon in Pfad 2 wird reflektiert oder genau umgekehrt. Die Quantensuperposition dieser Szenarien führt zu der Interferenz zwischen Zuständen, die physikalisch vertauschte Versionen voneinander sind, und offenbart die Teilchenaustauschphase ϕ_x. Der blaue Strahl wird von einem abgeschwächten Laser erzeugt und dient als Referenzsignal um die effektiven optischen Pfadlängenunterschiede, ϕ_1 und ϕ_2, zu bestimmen.

Im Beispiel hieße das, wenn jeder der Zwillinge den Raum aus der jeweils anderen Tür wieder verlässt. Bei Bosonen ändert sich nichts – bei Fermionen erhält die quantenmechanische Wellenfunktion, die die Teilchen beschreibt, einen Phasenschub, der auch Austauschphase genannt wird. „Im Zwillingsbeispiel kann man sich das vielleicht so vorstellen: Schicken wir die beiden Zwillinge im Gleichschritt in den Raum und kommen sie aus verschiedenen Türen wieder heraus, so sind sie weiterhin im Gleichschritt. Als Bosonen treten die Zwillinge mit demselben Bein voran aus dem Raum heraus, mit dem sie auch zuerst in Raum geschritten sind. Jedoch benötigen sie als Fermionen beide einen Schritt mehr und gehen beim Verlassen des Raumes nun mit dem anderen Bein voran“, so Benson. „Dass Photonen bosonisch sind, konnte bislang nur durch indirekte Messungen und mathematische Berechnungen gezeigt werden“, sagt Kurt Busch. „In unserem jüngsten Experiment haben wir die Teilchenaustauschphase von Photonen erstmals direkt gemessen und haben damit einen direkten Beleg für ihren bosonischen Charakter erbracht.“

Um die Austauschsymmetrie eines Zustandes für zwei identische Teilchen direkt nachzuweisen, hat das Team eine optische Apparatur mit einem Interferometer aufgebaut. Herzstück des Aufbaus – in der Größe eines kleinen Tisches – sind zwei Strahlteiler. Zwei Photonen wurden dann in das Interferometer geschickt und durch den Strahlteiler auf zwei verschiedene Wege geführt. Entlang einem der beiden Wege werden die Photonen miteinander vertauscht, während sie auf dem anderen unverändert bleiben. Am Ausgang des Interferometers wurden dann beide Photonen am zweiten Strahlteiler wieder überlagert. „Je nachdem, ob die Photonen bosonisch oder fermionisch sind, sind dann die beiden Photonen im Gleichschritt und verstärken sich oder sie sind außer Tritt und löschen sich aus“, erläutern die Physiker.

Zukünftige Verbesserungen des Interferometers werden ein neues Werkzeug für Präzisionsmessungen mit Quantenlicht bereitstellen. Gleichzeitig etabliert das Experiment eine neue Methode zur Erzeugung und Zertifizierung von Quanten-Zuständen von Licht. Dies ist sehr wichtig im neuen Gebiet der Quanteninformationsverarbeitung, auf deren Basis derzeit neuartige, wesentlich leistungsfähigere Computer entwickelt werden.


Direct observation of the particle exchange phase of photons
K. Tschernig, C. Müller, M. Smoor, T. Kroh, J. Wolters, O. Benson, K. Busch, and A. Perez-Leija
Nat. Photonics (2021), DOI: 10.1038/s41566-021-00818-7

 

 
Real-time optical distance sensing of up-conversion nanoparticles with a precision of 2.8 nanometers
  Sub-diffraction limited localization of fluorescent emitters is a major goal of microscopy imaging. It is of key importance for so-called super-resolution, a technique that was awarded the Nobel Prize in Chemistry in 2014. A cooperation of researchers in Australia, China, the USA and IRIS Adlershof have now demonstrated ultra-precise localization and tracking of fluorescent nanoparticles dispersed on a mirror. The many randomly oriented molecular dipoles in such up-conversion nanoparticles (UCNPs) interfere with their own mirror images and create unique, bright and position-sensitive patterns in the spatial domain.

The pattern can be detected in the far-field by a sensitive camera and was compared to a detailed and quantitative numerical simulation. In this way it was possible to localize individual particles with an accuracy of only 2.8 nm, a value which is smaller than 1/350 of the excitation wavelength.

The localization can be performed rapidly, and a single particle can be followed with a 50Hz frame rate. This is much faster than other self-interference-based methods based on mapping of the fluorescence spectrum. A special benefit of UCNPs is their high photo-stability and sensitivity, e.g. to temperature and PH. Therefore, the novel technique may be used for high-resolution multimodality single-particle tracking and sensing.

Axial Localization and Tracking of Self-interference Nanoparticles by Lateral Point Spread Functions
Y. Liu, Z. Zhou, F. Wang, G. Kewes, S. Wen, S. Burger, M. Ebrahimi Wakiani, P. Xi, J. Yang, X. Yang, O. Benson, and D. Jin
Nat. Commun. 12 (2021) 2019, DOI: 10.1038/s41467-021-22283-0

 

Inkjet-printed electrodes in OLEDs

Researchers in the HySPRINT joint lab Generative Manufacturing Processes for Hybrid Components (GenFab) of Humboldt-Universität zu Berlin (HU) and Helmholtz-Zentrum Berlin (HZB) have successfully implemented an ink produced by the Berlin-based company OrelTech in solution-processed organic light emitting diodes.

After inkjet printing the particle-free silver ink, an argon plasma is used to reduce the silver ions in the ink to metallic silver. “Because this process takes place at a low temperature, it is suitable for use with temperature-sensitive substrates, such as flexible plastic foils,” explains Dr. Konstantin Livanov, co-founder and CTO of OrelTech. The researchers fabricated organic light-emitting diodes employing the silver ink as a transparent conductive electrode on the flexible substrate PET. The resulting devices show comparable light output characteristics to those based on the otherwise widely used indium tin oxide (ITO). Crucially, however, the silver electrodes showed superior stability to ITO upon mechanical bending. Dr. Felix Hermerschmidt, senior researcher in the joint lab of HU and HZB, confirms, "The OLEDs based on the OrelTech ink remain intact at a bending radius at which the OLEDs based on ITO show breakage and fail.” This opens up several application opportunities of the printed devices. The work has been published in the journal Flexible and Printed Electronics and is available Open Access. GenFab, led by Prof. List-Kratochvil, who is a memnber of IRIS Adlershof, is moving into laboratories and offices in the new IRIS research building for further research and development work.

ITO-free OLEDs utilizing inkjet-printed and low temperature plasma-sintered Ag electrodes,
M. Hengge, K. Livanov, N. Zamoshchik, F. Hermerschmidt, and E..J. W. List-Kratochvil
Flex. Print. Electron. 6 (2021) 015009, DOI: 10.1088/2058-8585/abe604

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