In this study, we reanalyze the magnetic interactions in the Kitaev spin liquid candidate materials Na2IrO3, α-RuCl3, and α-Li2IrO3 using nonperturbative exact diagonalization methods. These methods are more appropriate given the relatively itinerant nature of the systems suggested in previous works. We treat all interactions up to third neighbours on equal footing. The computed terms reveal significant long range coupling, bond-anisotropy, and/or off-diagonal couplings which we argue naturally explain the observed ordered phases in these systems. Given these observations, the potential for realizing the spin-liquid state in real materials is analyzed, and synthetic challenges are defined and explained.

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 G. Jackeli and G. 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 (Na2IrO3, α-Li2IrO3, and α-RuCl3), three-dimensional Kitaev materials (β-and γ-Li2IrO3), and other potential candidates, completing the review with the list of open questions awaiting new insights.

The description of quantized collective excitations stands as a landmark in the quantum theory of condensed matter. A prominent example occurs in conventional magnets, which support bosonic magnons—quantized harmonic fluctuations of the ordered spins. In striking contrast is the recent discovery that strongly spin-orbital-coupled magnets, such as α-RuCl3, may display a broad excitation continuum inconsistent with conventional magnons. Due to incomplete knowledge of the underlying interactions unraveling the nature of this continuum remains challenging. The most discussed explanation refers to a coherent continuum of fractional excitations analogous to the celebrated Kitaev spin liquid. Here, we present a more general scenario. We propose that the observed continuum represents incoherent excitations originating from strong magnetic anharmonicity that naturally occurs in such materials. This scenario fully explains the observed inelastic magnetic response of α-RuCl3 and reveals the presence of nontrivial excitations in such materials extending well beyond the Kitaev state.

Recent studies have brought α-RuCl_{3} to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α-RuCl_{3}. These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.

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.

The bisdithiazolyl radical 1a is dimorphic, existing in two distinct molecular and crystal modifications. The α-phase crystallizes in the tetragonal space group P4̅2(1)m and consists of π-stacked radicals, tightly clustered about 4̅ points and running parallel to c. The β-phase belongs to the monoclinic space group P2(1)/c and, at ambient temperature and pressure, is composed of π-stacked dimers in which the radicals are linked laterally by hypervalent four-center six-electron S···S-S···S σ-bonds. Variable-temperature magnetic susceptibility χ measurements confirm that α-1a behaves as a Curie-Weiss paramagnet; the low-temperature variations in χ can be modeled in terms of a 1D Heisenberg chain of weakly coupled AFM S = (1)/(2) centers. The dimeric phase β-1a is essentially diamagnetic up to 380 K. Above this temperature there is a sharp hysteretic (T↑= 380 K, T↓ = 375 K) increase in χ and χT. Powder X-ray diffraction analysis of β-1a at 393 K has established that the phase transition corresponds to a dimer-to-radical conversion in which the hypervalent S···S-S···S σ-bond is cleaved. Variable-temperature and -pressure conductivity measurements indicate that α-1a behaves as a Mott insulator, but the ambient-temperature conductivity σ(RT) increases from near 10(-7) S cm(-1) at 0.5 GPa to near 10(-4) S cm(-1) at 5 GPa. The value of σ(RT) for β-1a (near 10(-4) S cm(-1) at 0.5 GPa) initially decreases with pressure as the phase change takes place, but beyond 1.5 GPa this trend reverses, and σ(RT) increases in a manner which parallels the behavior of α-1a. These changes in conductivity of β-1a are interpreted in terms of a pressure-induced dimer-to-radical phase change. High-pressure, ambient-temperature powder diffraction analysis of β-1a confirms such a transition between 0.65 and 0.98 GPa and establishes that the structural change involves rupture of the dimer in a manner akin to that observed at high temperature and ambient pressure. The response of the S···S-S···S σ-bond in β-1a to heat and pressure is compared to that of related dimers possessing S···Se-Se···S σ-bonds.

The synthesis and solid-state characterization of the resonance-stabilized heterocyclic thia/selenazyl radicals 1a-4a is described. While all the radicals crystallize in undimerized slipped pi-stacked arrays, the four crystal structures do not constitute an isomorphous set; crystals of 1a and 3a belong to the orthorhombic space group P2(1)2(1)2(1), while those of 2a and 4a belong to the monoclinic space group P2(1)/n. The origin of the structural dichotomy can be traced back to the packing of the radicals in the P2(1)/n structure, which maximizes intermolecular Se-Se' contacts. There are marked differences in the transport properties of the two groups. Variable temperature conductivity measurements reveal high, but activated, conductivity for the monoclinic pair (2a/4a), with sigma(298 K) > 10(-3) S cm(-1). The application of physical pressure increases the conductivity of both compounds, with sigma(298 K) at 5 GPa reaching 0.5 S cm(-1) for 2a and 2 S cm(-1) for 4a. Variable-temperature magnetic susceptibility measurements indicate strong antiferromagnetic (AFM) coupling for the monoclinic pair 2a and 4a, the behavior of which has been modeled in terms of a molecular-field modified 1D Heisenberg chain of AFM coupled S = 1/2 centers. Extended Huckel theory band structure calculations and density functional theory first principles methods have been used to develop a qualitative understanding of the conductive and magnetic properties of radicals of the type 1-4 as a function of the degree and direction of slippage of the radical pi-stacks.

In the pursuit of developing routes to enhance magnetic Kitaev interactions in α-RuCl3, as well as probing doping effects, we investigate the electronic properties of α-RuCl3 in proximity to graphene. We study α-RuCl3/graphene heterostructures via ab initio density functional theory calculations, Wannier projection and non-perturbative exact diagonalization methods. We show that α-RuCl3 becomes strained when placed on graphene and charge transfer occurs between the two layers, making α-RuCl3 (graphene) lightly electron-doped (hole-doped). This gives rise to an insulator to metal transition in α-RuCl3 with the Fermi energy located close to the bottom of the upper Hubbard band of the t2g manifold. These results suggest the possibility of realizing metallic and even exotic superconducting states. Moreover, we show that in the strained α-RuCl3 monolayer the Kitaev interactions are enhanced by more than 50% compared to the unstrained bulk structure. Finally, we discuss scenarios related to transport experiments in α-RuCl3/graphene heterostructures. arXiv:1908.04793v2 [cond-mat.str-el]