The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (Na ₂ IrO ₃ , α -Li ₂ IrO ₃ , and α -RuCl ₃ ), three-dimensional Kitaev materials ( β - and γ -Li ₂ IrO ₃ ), and other potential candidates, completing the review with the list of open questions awaiting new insights.

Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms. In memoriam, to Neil Ashcroft, who inspired us all.

Altermagnets are a novel class of magnetic materials, where magnetic order is staggered both in coordinate and momentum space. The metallic rutile oxide RuO₂, long believed to be a textbook Pauli paramagnet, recently emerged as a putative workhorse altermagnet when resonant X-ray and neutron scattering studies reported nonzero magnetic moments and long-range collinear order. While some experiments seem consistent with altermagnetism, magnetic order in RuO₂remains controversial. We show that RuO₂is nonmagnetic, both in bulk and thin film. Muon spectroscopy complemented by density-functional theory finds at most 1.14 × 10⁻⁴ μ_B/Ru in bulk and at most 7.5 × 10⁻⁴ μ_B/Ru in 11 nm epitaxial films, at our spectrometers’ detection limit, and dramatically smaller than previously reported neutron results that were used to rationalize altermagnetic behavior. Our own neutron diffraction measurements on RuO₂single crystals identify multiple scattering as the source for the false signal in earlier studies.

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.

Altermagnetism is a topic that has lately been gaining attention and the ${\mathrm{RuO}}_2$ compound is among one of the most studied altermagnetic candidates. However, the survey of available literature on ${\mathrm{RuO}}_2$ properties suggests that there is no consensus about the magnetism of this material. By performing density functional theory (DFT) calculations, we show that the electronic properties of stoichiometric ${\mathrm{RuO}}_2$ are described in terms of a Hubbard $U$, within $\mathrm{DFT}+U$, smaller than the value required to have magnetism. We further argue that Ru vacancies can actually aid the formation of a magnetic state in ${\mathrm{RuO}}_2$. This in turn suggests that a characterization of the amount of Ru vacancies in experimental samples might help the resolution of the controversy between the different experimental results.

Frustrated magnetism on the kagome lattice has been a fertile ground for rich and fascinating physics, ranging from experimental evidence of a spin liquid to theoretical predictions of exotic superconductivity. Among experimentally realized spin-$\frac{1}{2}$ kagome magnets, herbertsmithite, kapellasite, and haydeeite $\left[(\mathrm{Zn},\mathrm{Mg}){\mathrm{Cu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Cl}}_2\right]$ are all well described by a three-parameter Heisenberg model, but they exhibit distinctly different physics. We address the problem using a pseudofermion functional renormalization-group approach and analyze the low-energy physics in the experimentally accessible parameter range. Our analysis places kapellasite and haydeeite near the boundaries between magnetically ordered and disordered phases, implying that slight modifications could dramatically affect their magnetic properties. Inspired by this, we perform ab initio density functional theory calculations of (Zn,Mg,$\mathrm{Cd}){\mathrm{Cu}}_3$ $({\mathrm{OH})}_6{\mathrm{Cl}}_2$ at various pressures. Our results suggest that by varying pressure and composition one can traverse a paramagnetic regime between different magnetically ordered phases.