Soft materials are usually defined as materials made of mesoscopic entities, often self-organised, sensitive to thermal fluctuations and to weak perturbations. Archetypal examples are colloids, polymers, amphiphiles, liquid crystals, foams. The importance of soft materials in everyday commodity products, as well as in technological applications, is enormous, and controlling or improving their properties is the focus of many efforts. From a fundamental perspective, the possibility of manipulating soft material properties, by tuning interactions between constituents and by applying external perturbations, gives rise to an almost unlimited variety in physical properties. Together with the relative ease to observe and characterise them, this renders soft matter systems powerful model systems to investigate statistical physics phenomena, many of them relevant as well to hard condensed matter systems. Understanding the emerging properties from mesoscale constituents still poses enormous challenges, which have stimulated a wealth of new experimental approaches, including the synthesis of new systems with, e.g. tailored self-assembling properties, or novel experimental techniques in imaging, scattering or rheology. Theoretical and numerical methods, and coarse-grained models, have become central to predict physical properties of soft materials, while computational approaches that also use machine learning tools are playing a progressively major role in many investigations. This Roadmap intends to give a broad overview of recent and possible future activities in the field of soft materials, with experts covering various developments and challenges in material synthesis and characterisation, instrumental, simulation and theoretical methods as well as general concepts.

Recent advances in experimental and computational methods are increasing the quantity and complexity of generated data. This massive amount of raw data needs to be stored and interpreted in order to advance the materials science field. Identifying correlations and patterns from large amounts of complex data is being performed by machine learning algorithms for decades. Recently, the materials science community started to invest in these methodologies to extract knowledge and insights from the accumulated data. This review follows a logical sequence starting from density functional theory as the representative instance of electronic structure methods, to the subsequent high-throughput approach, used to generate large amounts of data. Ultimately, data-driven strategies which include data mining, screening, and machine learning techniques, employ the data generated. We show how these approaches to modern computational materials science are being used to uncover complexities and design novel materials with enhanced properties. Finally, we point to the present research problems, challenges, and potential future perspectives of this new exciting field.

Ambient energy harvesting has great potential to contribute to sustainable development and address growing environmental challenges. Converting waste energy from energy-intensive processes and systems (e.g. combustion engines and furnaces) is crucial to reducing their environmental impact and achieving net-zero emissions. Compact energy harvesters will also be key to powering the exponentially growing smart devices ecosystem that is part of the Internet of Things, thus enabling futuristic applications that can improve our quality of life (e.g. smart homes, smart cities, smart manufacturing, and smart healthcare). To achieve these goals, innovative materials are needed to efficiently convert ambient energy into electricity through various physical mechanisms, such as the photovoltaic effect, thermoelectricity, piezoelectricity, triboelectricity, and radiofrequency wireless power transfer. By bringing together the perspectives of experts in various types of energy harvesting materials, this Roadmap provides extensive insights into recent advances and present challenges in the field. Additionally, the Roadmap analyses the key performance metrics of these technologies in relation to their ultimate energy conversion limits. Building on these insights, the Roadmap outlines promising directions for future research to fully harness the potential of energy harvesting materials for green energy anytime, anywhere.

In recent years, the notion of 'Quantum Materials' has emerged as a powerful unifying concept across diverse fields of science and engineering, from condensed-matter and coldatom physics to materials science and quantum computing. Beyond traditional quantum materials such as unconventional superconductors, heavy fermions, and multiferroics, the field has significantly expanded to encompass topological quantum matter, two-dimensional materials and their van der Waals heterostructures, Moiré materials, Floquet time crystals, as well as materials and devices for quantum computation with Majorana fermions. In this Roadmap collection we aim to capture a snapshot of the most recent developments in the field, and to identify outstanding challenges and emerging opportunities. The format of the Roadmap, whereby experts in each discipline share their viewpoint and articulate their vision for quantum materials, reflects the dynamic and multifaceted nature of this research area, and is meant to encourage exchanges and discussions across traditional disciplinary boundaries. It is our hope that this collective vision will contribute to sparking new fascinating questions and activities at the intersection of materials science, condensed matter physics, device engineering, and quantum information, and to shaping a clearer landscape of quantum materials science as a new frontier of interdisciplinary scientific inquiry. We stress that this article is not meant to be a fully comprehensive review but rather an up-to-date snapshot of different areas of research on quantum materials with a minimal number of references focusing on the latest developments.

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin–momentum locked metallic edge states—both helical and chiral—surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps—up to a few hundred meV—promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.

The application of engineering tools and techniques to studying women's health, including biomaterials-based approaches, is a research field experiencing robust growth. Biomaterials are natural or synthetic materials used to repair or replace damaged tissues or organs or replicate an organ's physiological function. However, in addition to in vivo applications, there has been substantial recent interest in biomaterials for in vitro systems. Such artificial tissues and organs are employed in drug discovery, functional cell biological investigations, and basic research that would be ethically impossible to conduct in living women. This Roadmap is a collection of 11 sections written by leading and up-and-coming experts in this field who review and discuss four aspects of biomaterials for women's health. These include conditions that disproportionately but not exclusively affect women (e.g. breast cancer), conditions unique to female reproductive organs, in both non-pregnant and pregnant states, and sex differences in non-reproductive tissues (e.g. the cardiovascular system). There is a strong need to develop this exciting field, with the potential to materially influence women's lives worldwide.

Over the past 150 years, our ability to produce and transform engineered materials has been responsible for our current high standards of living, especially in developed economies. However, we must carefully think of the effects our addiction to creating and using materials at this fast rate will have on the future generations. The way we currently make and use materials detrimentally affects the planet Earth, creating many severe environmental problems. It affects the next generations by putting in danger the future of the economy, energy, and climate. We are at the point where something must drastically change, and it must change now. We must create more sustainable materials alternatives using natural raw materials and inspiration from nature while making sure not to deplete important resources, i.e. in competition with the food chain supply. We must use less materials, eliminate the use of toxic materials and create a circular materials economy where reuse and recycle are priorities. We must develop sustainable methods for materials recycling and encourage design for disassembly. We must look across the whole materials life cycle from raw resources till end of life and apply thorough life cycle assessments (LCAs) based on reliable and relevant data to quantify sustainability. We need to seriously start thinking of where our future materials will come from and how could we track them, given that we are confronted with resource scarcity and geographical constrains. This is particularly important for the development of new and sustainable energy technologies, key to our transition to net zero. Currently 'critical materials' are central components of sustainable energy systems because they are the best performing. A few examples include the permanent magnets based on rare earth metals (Dy, Nd, Pr) used in wind turbines, Li and Co in Li-ion batteries, Pt and Ir in fuel cells and electrolysers, Si in solar cells just to mention a few. These materials are classified as 'critical' by the European Union and Department of Energy. Except in sustainable energy, materials are also key components in packaging, construction, and textile industry along with many other industrial sectors. This roadmap authored by prominent researchers working across disciplines in the very important field of sustainable materials is intended to highlight the outstanding issues that must be addressed and provide an insight into the pathways towards solving them adopted by the sustainable materials community. In compiling this roadmap, we hope to aid the development of the wider sustainable materials research community, providing a guide for academia, industry, government, and funding agencies in this critically important and rapidly developing research space which is key to future sustainability.

Artificial intelligence (AI) and additive manufacturing (AM) are both disruptive new technologies. AI has entered many aspects of our lives, but has not been fully realized in the world of AM. Because of the vast amount of data and the digital nature of the technology, AM offers tremendous opportunities in machine learning (ML) and consequently AI. This paper provides a vantage point view of the applications of ML and AI in AM, and specifically in powder bed AM technology. The types of data, sources of data, potential variabilities in experimental and simulation data, and the applicability of these data in ML algorithms are discussed. Several new ideas are presented where fusing these two transformative technologies can potentially have a profound impact on how AM is applied in different fields. A vision on the potential direction of AM to fully realize AI's advantage is provided.

This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to contributions in high-energy physics by Dirac. The review starts by a presentation of the Dirac magnetic monopole, goes on with the Berry phase in a two-level system and the geometrical/topological band theory for Bloch electrons in crystals. Next, specific examples of tight-binding models giving rise to lattice versions of the Dirac equation in various space dimension are presented: in 1D (Su–Schrieffer–Heeger (SSH) and Rice–Mele models), 2D (graphene, boron nitride, Haldane model) and 3D (Weyl semi-metals). The focus is on topological insulators and topological semi-metals. The latter have a Fermi surface that is characterized as a topological defect. For topological insulators, the two alternative view points of twisted fiber bundles and of topological textures are developed. The minimal mathematical background in topology (essentially on homotopy groups and fiber bundles) is provided when needed. Topics rarely reviewed include: periodic versus canonical Bloch Hamiltonian (basis I/II issue), Zak versus Berry phase, the vanishing electric polarization of the SSH model and Dirac insulators.

Wide and ultrawide-bandgap (U/WBG) materials have garnered significant attention within the semiconductor device community due to their potential to enhance device performance through their substantial bandgap properties. These exceptional material characteristics can enable more robust and efficient devices, particularly in scenarios involving high power, high frequency, and extreme environmental conditions. Despite the promising outlook, the physics of UWBG materials remains inadequately understood, leading to a notable gap between theoretical predictions and experimental device behavior. To address this knowledge gap and pinpoint areas where further research can have the most significant impact, this review provides an overview of the progress and limitations in U/WBG materials. The review commences by discussing Gallium Nitride, a more mature WBG material that serves as a foundation for establishing fundamental concepts and addressing associated challenges. Subsequently, the focus shifts to the examination of various UWBG materials, including AlGaN/AlN, Diamond, and Ga₂O₃. For each of these materials, the review delves into their unique properties, growth methods, and current state-of-the-art devices, with a primary emphasis on their applications in power and radio-frequency electronics.

Valleytronics uses valleys, a novel quantum degree of freedom, to encode information. It combines other degrees of freedom, such as charge and spin, to produce a more comprehensive, stable, and efficient information processing system. Valleytronics has become an intriguing field in condensed matter physics due to the emergence of new two-dimensional materials in recent years. However, in nonmagnetic valleytronic materials, the valley polarization is transient and the depolarization occurs once the external excitation is withdrawn. Introduction of magnetic field is an effective approach to realizing the spontaneous valley polarization by breaking the time-reversal symmetry. In hexagonal magnetic valleytronic materials, the inequivalent valleys at the K and –K(K') Dirac cones have asymmetric energy gaps and Berry curvatures. The time-reversal symmetry in nonmagnetic materials can be broken by applying an external magnetic field, adding a magnetic substrate or doping magnetic atoms. Recent theoretical studies have demonstrated that valleytronic materials with intrinsic ferromagnetism, now termed as ferrovalley materials, exhibit spontaneous valley polarization without the need for external fields to maintain the polarization. The coupling of the valley and spin degrees of freedom enables stable and unequal distribution of electrons in the two valleys and thus facilitating nonvolatile information storage. Hence, ferrovalley materials are promising materials for valleytronic devices. In this review, we first briefly overview valleytronics and its related properties, the ways to realize valley polarization in nonmagnetic valleytronic materials. Then we focus on the recent developments in two-dimensional ferrovalley materials, which can be classified according to their molecular formula and crystal structure: MX₂; M(XY)₂, M(XY₂) and M(XYZ)₂; M₂X₃, M₃X₈ and MNX₆; MNX₂Y₂, M₂X₂Y₆ and MNX₂Y₆; and the Janus structure ferrovalley materials. In the inequivalent valleys, the Berry curvatures have opposite signs with unequal absolute values, leading to anomalous valley Hall effect. When the valley polarization is large, the ferrovalleys can be selectively excited even with unpolarized light. Intrinsic valley polarization in two-dimensional ferrovalley materials is of great importance. It opens a new avenue for information-related applications and hence is under rapid development.

Finding the ground-state structure with minimum energy is paramount to designing any material. In ABO₃-type perovskite oxides with Pnma symmetry, the lowest energy phase is driven by an inherent trilinear coupling between the two primary order parameters such as rotation and tilt with antiferroelectric displacement of the A-site cations as established via hybrid improper ferroelectric mechanism. Conventionally, finding the relevant mode coupling driving phase transition requires performing first-principles calculations which is computationally time-consuming as well as expensive. It involves following an intuitive iterative hit and trial method of (a) adding two or multiple mode vectors, followed by (b) evaluating which combination would lead to the ground-state energy. In this study, we show how a hypothesis-driven active learning framework can identify suitable mode couplings within the Landau free energy expansion with minimal information on amplitudes of modes for a series of double perovskite oxides with A-site layered, columnar and rocksalt ordering. This scheme is expected to be applicable universally for understanding atomistic mechanisms derived from various structural mode couplings behind functionalities, for e.g. polarization, magnetization and metal–insulator transitions.

The ability to tune band gaps of semiconductors is important for many optoelectronics applications including photocatalysis. A common approach to this is doping, but this often has the disadvantage of introducing defect states in the electronic structure that can result in poor charge mobility and increased recombination losses. In this work, density functional theory calculations are used to understand how co-doping and solid solution formation can allow tuning of semiconductor band gaps through indirect effects. The addition of ZnS to GaP alters the local environments of the Ga and P atoms, resulting in shifts in the energies of the P and Ga states that form the valence and conduction band edges, and hence changes the band gap without altering which atoms form the band edges, providing an explanation for previous experimental observations. Similarly, N doping of ZnO is known from previous experimental work to reduce the band gap and increase visible-light absorption; here we show that, when co-doped with Al, the Al changes the local environment of the N atoms, providing further control of the band gap without introducing new states within the band gap or at the band edges, while also providing an energetically more favourable state than N-doped ZnO. Replacing Al with elements of different electronegativity is an additional tool for band gap tuning, since the different electronegativities correspond to different effects on the N local environment. The consistency in the parameters identified here that control the band gaps across the various systems studied indicates some general concepts that can be applied in tuning the band gaps of semiconductors, without or only minimally affecting charge mobility.

The integration of graph-based representations with machine learning methodologies is transforming the landscape of material discovery, offering a flexible approach for modelling a variety of materials, from molecules and nanomaterials to expansive three-dimensional bulk materials. Nonetheless, the literature often lacks a systematic exploration from the perspective of material dimensionality. While it is important to design representations and algorithms that are universally applicable across species, it is intuitive for material scientists to align the underlying patterns between dimensionality and the characteristics of the employed graph descriptors. In this review, we provide an overview of the graph representations as inputs to machine learning models and navigate the recent applications, spanning the diverse range of material dimensions. This review highlights both persistent gaps and innovative solutions to these challenges, emphasising the pressing need for larger benchmark datasets and leveraging graphical patterns. As graph-based machine learning techniques evolve, they present a promising frontier for accurate, scalable, and interpretable material applications.

The La–Co co-substituted magnetoplumbite-type (M-type) ferrites AFe₁₂O₁₉ (A = Ca, Sr and Ba, ion sizes Ca²⁺$\lt$ Sr²⁺$\lt$ Ba²⁺) with Co compositions around 0.2 have been subjected to ⁵⁹Co-NMR. The results show that Co occupies the 4f₁, 2a and 12k sites, and that the smaller the A ion, the more Co tends to occupy the 4f₁ minority spin site, which is effective in enhancing both uniaxial anisotropy and magnetisation. First-principles total energy calculations based on density functional theory (DFT) of undoped AFe₁₂O₁₉ and a supercell ($2 \times 2 \times 1$ of the unit cell) in which 1/96 of Fe³⁺ is replaced by Co²⁺ were performed to predict the stable structure and Co occupancy sites. The results show that regardless of A, Co is most stable when it occupies the 4f₁ site, followed by the 2a and 12k sites with energy differences on the order of 100 meV, and Co practically does not occupy the 2b and 4f₂ sites. As the A ion becomes smaller, the energy difference when Co occupies each Fe site tends to increase, and the Co occupancy of the 4f₁ site also increases. The site selectivity of Co can be roughly explained as a result of the difference in uniaxial strain along the c-axis associated with the difference in A. However, the influence of the A ion differs between the R and S blocks and the local strain also has a secondary effect on the Co distribution. Based on these results, the guidelines for improving the performance (anisotropy and magnetisation) of La–Co co-substituted M-type ferrite magnets with a limited amount of Co can be summarised as follows: It is effective to select as small A ions as possible and to post-anneal at low temperature or cool slowly to concentrate Co at the 4f₁ site in tetrahedral coordination.

Valleytronics uses valleys, a novel quantum degree of freedom, to encode information. It combines other degrees of freedom, such as charge and spin, to produce a more comprehensive, stable, and efficient information processing system. Valleytronics has become an intriguing field in condensed matter physics due to the emergence of new two-dimensional materials in recent years. However, in nonmagnetic valleytronic materials, the valley polarization is transient and the depolarization occurs once the external excitation is withdrawn. Introduction of magnetic field is an effective approach to realizing the spontaneous valley polarization by breaking the time-reversal symmetry. In hexagonal magnetic valleytronic materials, the inequivalent valleys at the K and –K(K') Dirac cones have asymmetric energy gaps and Berry curvatures. The time-reversal symmetry in nonmagnetic materials can be broken by applying an external magnetic field, adding a magnetic substrate or doping magnetic atoms. Recent theoretical studies have demonstrated that valleytronic materials with intrinsic ferromagnetism, now termed as ferrovalley materials, exhibit spontaneous valley polarization without the need for external fields to maintain the polarization. The coupling of the valley and spin degrees of freedom enables stable and unequal distribution of electrons in the two valleys and thus facilitating nonvolatile information storage. Hence, ferrovalley materials are promising materials for valleytronic devices. In this review, we first briefly overview valleytronics and its related properties, the ways to realize valley polarization in nonmagnetic valleytronic materials. Then we focus on the recent developments in two-dimensional ferrovalley materials, which can be classified according to their molecular formula and crystal structure: MX₂; M(XY)₂, M(XY₂) and M(XYZ)₂; M₂X₃, M₃X₈ and MNX₆; MNX₂Y₂, M₂X₂Y₆ and MNX₂Y₆; and the Janus structure ferrovalley materials. In the inequivalent valleys, the Berry curvatures have opposite signs with unequal absolute values, leading to anomalous valley Hall effect. When the valley polarization is large, the ferrovalleys can be selectively excited even with unpolarized light. Intrinsic valley polarization in two-dimensional ferrovalley materials is of great importance. It opens a new avenue for information-related applications and hence is under rapid development.

The integration of graph-based representations with machine learning methodologies is transforming the landscape of material discovery, offering a flexible approach for modelling a variety of materials, from molecules and nanomaterials to expansive three-dimensional bulk materials. Nonetheless, the literature often lacks a systematic exploration from the perspective of material dimensionality. While it is important to design representations and algorithms that are universally applicable across species, it is intuitive for material scientists to align the underlying patterns between dimensionality and the characteristics of the employed graph descriptors. In this review, we provide an overview of the graph representations as inputs to machine learning models and navigate the recent applications, spanning the diverse range of material dimensions. This review highlights both persistent gaps and innovative solutions to these challenges, emphasising the pressing need for larger benchmark datasets and leveraging graphical patterns. As graph-based machine learning techniques evolve, they present a promising frontier for accurate, scalable, and interpretable material applications.

The progress of machine learning (ML) in the past years has opened up new opportunities to the design of auxetic metamaterials. However, successful implementation of ML algorithms remains challenging, particularly for complex problems such as domain performance prediction and inverse design. In this paper, we first reviewed classic auxetic designs and summarized their variants in different applications. The enormous variant design space leads to challenges using traditional design or topology optimization. Therefore, we also investigated how ML techniques can help address design challenges of auxetic metamaterials and when researchers should deploy them. The theories behind the techniques are explained, along with practical application examples from the analyzed literature. The advantages and limitations of different ML algorithms are discussed and trends in the field are highlighted. Finally, two practical problems of ML-aided design, design scales and data collection are discussed.

Wide and ultrawide-bandgap (U/WBG) materials have garnered significant attention within the semiconductor device community due to their potential to enhance device performance through their substantial bandgap properties. These exceptional material characteristics can enable more robust and efficient devices, particularly in scenarios involving high power, high frequency, and extreme environmental conditions. Despite the promising outlook, the physics of UWBG materials remains inadequately understood, leading to a notable gap between theoretical predictions and experimental device behavior. To address this knowledge gap and pinpoint areas where further research can have the most significant impact, this review provides an overview of the progress and limitations in U/WBG materials. The review commences by discussing Gallium Nitride, a more mature WBG material that serves as a foundation for establishing fundamental concepts and addressing associated challenges. Subsequently, the focus shifts to the examination of various UWBG materials, including AlGaN/AlN, Diamond, and Ga₂O₃. For each of these materials, the review delves into their unique properties, growth methods, and current state-of-the-art devices, with a primary emphasis on their applications in power and radio-frequency electronics.

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin–momentum locked metallic edge states—both helical and chiral—surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps—up to a few hundred meV—promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.