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We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.
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Recent experiments on kagome metals AV_{3}Sb_{5} (A=Cs,Rb,K) indicated spontaneous time-reversal symmetry breaking in the charge density wave state in the absence of static magnetization. The loop current order (LCO) is proposed as its cause, but a microscopic model explaining the emergence of LCO through electronic correlations has not been firmly established. We show that the coupling between van Hove singularities with distinct mirror symmetries is a key ingredient to generate LCO ground state. By constructing an effective model, we find that when multiple van Hove singularities with opposite mirror eigenvalues are close in energy, the nearest-neighbor electron repulsion favors a ground state with coexisting LCO and charge bond order. It is then demonstrated that this mechanism applies to the kagome metals AV_{3}Sb_{5}. Our findings provide an intriguing mechanism of LCO and pave the way for a deeper understanding of complex quantum phenomena in kagome systems.
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The simulation of fermionic relativistic physics, e.g., Dirac and Weyl physics, has led to the discovery of many unprecedented phenomena in photonics, of which the optical-frequency realization is, however, still challenging. Here, surprisingly, we discover that the woodpile photonic crystals commonly used for optical frequency applications host exotic fermion-like relativistic degeneracies: a Dirac nodal line and a fourfold quadratic point, as protected by the nonsymmorphic crystalline symmetry. Deforming the woodpile photonic crystal leads to the emergence of type-II Dirac points from the fourfold quadratic point. Such type-II Dirac points can be detected by its anomalous refraction property which is manifested as a giant birefringence in a slab setup. Our findings provide a promising route towards 3D optical Dirac physics in all-dielectric photonic crystals.
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We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra "Γ term," using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, although the exact symmetry group of the system is discrete, the low energy theory is described by an emergent SU(2)_{1} Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation functions exhibit SU(2) breaking prefactors, even though the exponents and the logarithmic corrections are consistent with the SU(2)_{1} predictions. A modified non-Abelian bosonization formula is proposed to capture such exotic emergent "partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an O_{h}âD_{4} spontaneous symmetry breaking.
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Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice described by the Kane-Mele-Hubbard model has not been identified. Here we report a novel approach to realize a 2D honeycomb-lattice narrow-band system with strongly interacting 5d electrons. We engineer a well-known triangular lattice 2D Mott insulator 1T-TaS_{2} into a honeycomb lattice utilizing an adsorbate superstructure. Potassium (K) adatoms at an optimum coverage deplete one-third of the unpaired d electrons and the remaining electrons form a honeycomb lattice with a very small hopping. Ab initio calculations show extremely narrow Z_{2} topological bands mimicking the Kane-Mele model. Electron spectroscopy detects an order of magnitude bigger charge gap confirming the substantial electron correlation as confirmed by dynamical mean field theory. It could be the first artificial Mott insulator with a finite spin Chern number.
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The spin S=1/2 Kitaev honeycomb model has attracted significant attention since emerging candidate materials have provided a playground to test non-Abelian anyons. The Kitaev model with higher spins has also been theoretically studied, as it may offer another path to a quantum spin liquid. However, a microscopic route to achieve higher spin Kitaev models in solid state materials has not been rigorously derived. Here we present a theory of the spin S=1 Kitaev interaction in two-dimensional edge-shared octahedral systems. Essential ingredients are strong spin-orbit coupling in anions and strong Hund's coupling in transition metal cations. The S=1 Kitaev and ferromagnetic Heisenberg interactions are generated from superexchange paths. Taking into account the antiferromagnetic Heisenberg term from direct-exchange paths, the Kitaev interaction dominates the physics of the S=1 system. Using an exact diagonalization technique, we show a finite regime of S=1 spin liquid in the presence of the Heisenberg interaction. Candidate materials are proposed, and generalization to higher spins is discussed.
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Three-dimensional (3D) topological Dirac semimetals (TDSs) are rare but important as a versatile platform for exploring exotic electronic properties and topological phase transitions. A quintessential feature of TDSs is 3D Dirac fermions associated with bulk electronic states near the Fermi level. Using angle-resolved photoemission spectroscopy, we have observed such bulk Dirac cones in epitaxially grown α-Sn films on InSb(111), the first such TDS system realized in an elemental form. First-principles calculations confirm that epitaxial strain is key to the formation of the TDS phase. A phase diagram is established that connects the 3D TDS phase through a singular point of a zero-gap semimetal phase to a topological insulator phase. The nature of the Dirac cone crosses over from 3D to 2D as the film thickness is reduced.
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In 5d Ir oxides with an interplay of spin-orbit coupling and electron correlations, we have tailored a spin-orbital magnetic insulator out of a semimetal SrIrO(3) by tuning the structure through superlattices [(SrIrO(3))(m), SrTiO(3)] (m=1,2,3,4, and ∞). We observed the systematic decrease of the magnetic ordering temperature and the resistivity as a function of m. The transition from the semimetal to the insulator is found to be closely linked to the appearance of magnetism at m≃3. Long range magnetic ordering was realized even in the m=1 single layer superlattice, implying that the design and realization of novel electronic phases is feasible at the level of a single atomic layer in complex Ir oxides.
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We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems [corrected]. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in x-ray scattering experiments. Various other experimental signatures of the exotic cluster Mott insulator are discussed in light of candidate materials with partially filled bands on the pyrochlore lattice.
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We explore possible superconducting states in t(2g) multiorbital correlated electron systems with strong spin-orbit coupling (SOC). In order to study such systems in a controlled manner, we employ large-scale dynamical mean-field theory (DMFT) simulations with the hybridization expansion continuous-time quantum Monte Carlo (CTQMC) impurity solver. To determine the pairing symmetry, we go beyond the local DMFT formalism using parquet equations to introduce the momentum dependence in the two-particle vertex and correlation functions. In the strong SOC limit, a singlet, d-wave pairing state in the electron-doped side of the phase diagram is observed at weak Hund's coupling, which is triggered by antiferromagnetic fluctuations. When the Hund's coupling is comparable to SOC, a twofold degenerate, triplet p-wave pairing state with relatively high transition temperature emerges in the hole-doped side of the phase diagram, which is associated with enhanced charge fluctuations. Experimental implications to doped Sr2IrO4 are discussed.
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Recently, realizations of Kitaev physics have been sought in the A2IrO3 family of honeycomb iridates, originating from oxygen-mediated exchange through edge-shared octahedra. However, for the jeff=1/2 Mott insulator in these materials, exchange from direct d-orbital overlap is relevant, and it was proposed that a Heisenberg term should be added to the Kitaev model. Here, we provide the generic nearest-neighbor spin Hamiltonian when both oxygen-mediated and direct overlap are present, containing a bond-dependent off-diagonal exchange in addition to Heisenberg and Kitaev terms. We analyze this complete model using a combination of classical techniques and exact diagonalization. Near the Kitaev limit, we find new magnetic phases, 120° and incommensurate spiral order, as well as extended regions of zigzag and stripy order. Possible applications to Na2IrO3 and Li2IrO3 are discussed.
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The EtMe(3)P and EtMe(3)Sb triangular organic salts are distinguished from other Pd[(dmit)(2)] based salts, as they display valence bond and no long-range order, respectively. Under pressure, a superconducting phase is revealed in EtMe(3)P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperature phase diagram manifests a remarkable resemblance to the phase diagram of the EtMe(3)P salt, where the reentrant transition of insulator-metal-insulator type can be explained by an entropy difference between the metal and U(1) spin liquid. We predict different temperature dependence of the specific heat between the spin liquid and metal.
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Recent quantum oscillation measurements in high-temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here, we explain the observations with the theory that the alleged normal state exhibits a hidden order, the d-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle pi/2, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but we also touch on the consequences if the order were to incommensurate. It is shown that whereas commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets.
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A remarkable mystery of the copper oxide high-transition-temperature (T(c)) superconductors is the dependence of T(c) on the number of CuO2 layers, n, in the unit cell of a crystal. In a given family of these superconductors, T(c) rises with the number of layers, reaching a peak at n = 3, and then declines: the result is a bell-shaped curve. Despite the ubiquity of this phenomenon, it is still poorly understood and attention has instead been mainly focused on the properties of a single CuO2 plane. Here we show that the quantum tunnelling of Cooper pairs between the layers simply and naturally explains the experimental results, when combined with the recently quantified charge imbalance of the layers and the latest notion of a competing order nucleated by this charge imbalance that suppresses superconductivity. We calculate the bell-shaped curve and show that, if materials can be engineered so as to minimize the charge imbalance as n increases, T(c) can be raised further.
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Elementary excitations in entangled states such as quantum spin liquids may exhibit exotic statistics different from those obeyed by fundamental bosons and fermions. Non-Abelian anyons exist in a Kitaev spin liquid-the ground state of an exactly solvable model. A smoking-gun signature of these excitations, namely a half-integer quantized thermal Hall conductivity, was recently reported in α-RuCl3. While fascinating, a microscopic theory for this phenomenon remains elusive because the pure Kitaev model cannot display this effect in an intermediate magnetic field. Here we present a microscopic theory of the Kitaev spin liquid emerging between the low- and high-field states. Essential to this result is an antiferromagnetic off-diagonal symmetric interaction which allows the Kitaev spin liquid to protrude from the ferromagnetic Kitaev limit under a magnetic field. This generic model displays a strong field anisotropy, and we predict a wide spin liquid regime when the field is perpendicular to the honeycomb plane.
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Dimensional tunability from two dimensions to one dimension is demonstrated for the first time using an artificial superlattice method in synthesizing 1D stripes from 2D layered materials. The 1D confinement of layered Sr2 IrO4 induces distinct 1D quantum-confined electronic states, as observed from optical spectroscopy and resonant inelastic X-ray scattering. This 1D superlattice approach is generalizable to a wide range of layered materials.
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Since topological insulators were theoretically predicted and experimentally observed in semiconductors with strong spin-orbit coupling, increasing attention has been drawn to topological materials that host exotic surface states. These surface excitations are stable against perturbations since they are protected by global or spatial/lattice symmetries. Following the success in achieving various topological insulators, a tempting challenge now is to search for metallic materials with novel topological properties. Here we predict that orthorhombic perovskite iridates realize a new class of metals dubbed topological crystalline metals, which support zero-energy surface states protected by certain lattice symmetry. These surface states can be probed by photoemission and tunnelling experiments. Furthermore, we show that by applying magnetic fields, the topological crystalline metal can be driven into other topological metallic phases, with different topological properties and surface states.
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Electronic-nematic phases are broadly characterized by spontaneously broken rotational symmetry. Although they have been widely recognized in the context of high temperature cuprates, bilayer ruthenates, and iron-based superconductors, the focus so far has been exclusively on the uniform nematic phase. Recently, however, it was proposed that on a square lattice a nematic instability in the d-wave charge channel could lead to a spatially modulated nematic state, where the modulation vector q is determined by the relative location of the Fermi level to the van Hove singularity. Interestingly, this finite-q nematic (nematic stripe) phase has also been identified as an additional leading instability that is as strong as the superconducting instability near the onset of spin density wave order. Here, we study the electrical conductivity tensor in the modulated nematic phase for a general modulation vector. Our results can be used to identify nematic stripe phases in correlated materials.
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Recent experiments on the "hyperkagome" lattice system Na4Ir3O8 have demonstrated that it is a rare example of a three-dimensional spin-1/2 frustrated antiferromagnet. We investigate the role of quantum fluctuations as the primary mechanism lifting the macroscopic degeneracy inherited by classical spins on this lattice. In the semiclassical limit we predict, based on large-N calculations, that an unusual q[over -->]=0 coplanar magnetically ordered ground state is stabilized with no local zero modes that correspond to local deformations of the spin configurations. This phase melts in the quantum limit and a gapped topological Z2 spin liquid phase emerges. In the vicinity of this quantum phase transition, we study the dynamic spin structure factor and comment on the relevance of our results for future neutron scattering experiments.