Editorial: Symmetry-Guided Rational Design and Control of Quantum Matter with New Functionality

Nicole Benedek ^1* Milan Radovic ^2* Berit Hansen Goodge ^3* Alberto De La Torre ^4*

• ¹ Cornell University, Ithaca, New York, United States
• ² Paul Scherrer Institut (PSI), Villigen, Switzerland
• ³ Max Planck Institute for Chemical Physics of Solids, Dresden, Lower Saxony, Germany
• ⁴ Northeastern University, Boston, United States

Quantum materials provide a vibrant playground to challenge our comprehension of complex emergent phenomena and a vital foundation for disruptive nextgeneration technologies. Ongoing advances in rational material design, synthesis approaches, ultrafast optical control, and experimental and theoretical characterization tools can be deployed in a continuous dynamic feedback loop to probe the fundamental nature of complex matter and achieve tunable control of their functional properties. This Research Topic showcases recent work in the design and control of quantum materials, including new observations, predictions, and methodologies that further our current understanding of their emerging properties.In particular, our collection includes four articles on a wide range of topics, from prediction to synthesis to understanding new materials. Abarca Morales introduces a framework designed to analyze and predict materials' structures and symmetries, especially how they evolve under strain. By focusing on the interactions and arrangements of four interconnected octahedra -a common motif in many quantum materials -, this model provides insights into the emergence of specific material functionalities and facilitates the rational design of compounds with desired characteristics. Focusing on materials properties, Han et al. reviews the potential of ABO3 transition metal oxides (TMOs) in spintronic applications. Emphasis is put on their unique electronic structures and quantum states, discussing how the interplay between strong spin-orbit coupling and electronic correlations leads to efficient charge-spin interconversion. It highlights strategies for tuning these properties through epitaxial strain and heterostructure engineering. Nixon et al. presents a new study on superconducting mercurides of strontium, offering valuable insights into superconductivity in mercury-rich compounds and addressing the challenges of synthesizing these materials by studying their structural and superconducting properties. Finally, Romaguera et al. focuses on the design principles for stabilizing magnetoelectric (ME) spiral phases at room temperature. Recent experimental observations in Cu/Febased layered perovskites demonstrate how chemical disorder and control over specific interatomic distances can stabilize magnetic spiral phases at temperatures as high as 400 K. The review presents strategies for designing materials with ME spirals suitable for practical applications. Altogether, this research collection reflects the breadth of knowledge needed to tackle the challenges and opportunities in the design and control of quantum materials.These articles underscore the transformative power of combining prediction and experiment to push the boundaries of what is possible in quantum science. Other examples not shown in this collection include the dimensionality control in thin films of Ruddlesden-Popper transition metal oxides, which have emerged as a key platform to control their emergent properties [1-3]. Topotactic reactions in Kitaev iridates have provided a versatile approach to manipulate and tailor their magnetic and electronic properties towards the elusive Quantum Spin Liquid limit [4] Additionally, machine learning is rapidly transforming the field of quantum materials by enabling predictive capabilities that were previously unattainable. For example, predictions involving materials such as LiBC highlight the potential to establish novel superconducting phases [5,6]. By leveraging large datasets and advanced algorithms, machine learning provides a powerful tool to guide experiments and theory, bridging the gap between materials discovery and functional applications.We are deeply grateful to the authors, reviewers, and editors who have made this Research Topic possible. Their collective efforts have resulted in a diverse and impactful collection of works highlighting the importance of symmetry-guided approaches in advancing quantum materials. We hope this collection inspires new ideas and directions in the discovery, engineering, and functionalization of quantum materials for next-generation computing, sensing, and energy technologies.[1] Bongjae Kim, Peitao Liu, and Cesare Franchini, "Dimensionality-strain phase diagram of strontium iridates," Phys. Rev. B 95, 115111 (2017).[2] Grace A. Pan, Qi Song, Dan Ferenc Segedin, Myung-Chul