We investigate the interplay between the strong correlation and the spin-orbit coupling in the Kane-Mele-Hubbard model and obtain the qualitative phase diagram via the variational cluster approach. We identify, through an increase of the Hubbard U, the transition from the topological band insulator to either the spin liquid phase or the easy-plane antiferromagnetic insulating phase, depending on the strength of the spin-orbit coupling. A nontrivial evolution of the bulk bands in the topological quantum phase transition is also demonstrated.

We study the spin-wave excitations in α-RuCl3 by the spin-wave theory. Starting from the fiveorbital Hubbard model and the perturbation theory, we derive an effective isospin-1/2 model in the large Hubbard (U ) limit. Based on the energy-band structure calculated from the first-principle method, we find that the effective model can be further reduced to the K-Γ model containing a ferromagnetic nearest-neighbor (NN) Kitaev interaction (K) and a NN off-diagonal exchange interaction (Γ). With the spin-wave theory, we find that the K-Γ model can give magnetic excitations which is consistent with the recent neutron scattering experiments.

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Topological magnons are emergent quantum spin excitations featured by magnon bands crossing linearly at the points dubbed nodes, analogous to fermions in topological electronic systems. Experimental realisation of topological magnons in three dimensions has not been reported so far. Here, by measuring spin excitations (magnons) of a three-dimensional antiferromagnet Cu3TeO6 with inelastic neutron scattering, we provide direct spectroscopic evidence for the coexistence of symmetry-protected Dirac and triply degenerate nodes, the latter involving three-component magnons beyond the Dirac–Weyl framework. Our theoretical calculations show that the observed topological magnon band structure can be well described by the linear-spin-wave theory based on a Hamiltonian dominated by the nearest-neighbour exchange interaction J1. As such, we showcase Cu3TeO6 as an example system where Dirac and triply degenerate magnonic nodal excitations coexist, demonstrate an exotic topological state of matter, and provide a fresh ground to explore the topological properties in quantum materials.

The possible ground states of the undoped and doped Kitaev-Heisenberg model on a triangular lattice are studied. For the undoped system, a combination of the numerical exact diagonalization calculation and the four-sublattice transformation analysis suggests one possible exotic phase and four magnetically ordered phases, including a collinear stripe pattern and a noncollinear spiral pattern in the global phase diagram. The exotic phase near the antiferromagnetic (AF) Kitaev point is further investigated using the Schwinger-fermion mean-field method, and we obtain an energetically favorable Z 2 chiral spin liquid with a Chern number ±2 as a promising candidate. At finite doping, we find that the AF Heisenberg coupling supports an s-wave or a + − d d i x y xy 2 2 -wave superconductivity (SC), while the AF and the ferromagnetic Kitaev interactions favor a + − d d i x y xy 2 2 -wave SC and a time-reversal invariant topological p-wave SC, respectively. Possible experimental realizations and related candidate materials are also discussed. IntroductionRecently, there has been enormous interest in the physics of the spin-1/2 Kitaev model on a honeycomb lattice [1], which has an exact Z 2 spin-liquid (SL) ground state (GS) supporting fractionalized excitations. One possible route to realize this highly anisotropic spin model is to include a strong relativistic spin-orbit coupling (SOC) in Mott insulators [2,3]. Indeed, the interplay of SOC and electron interactions [4][5][6][7][8] gives rise to many novel phases [9][10][11][12][13], especially for the so-called relativistic Mott insulators (RMIs) whose physics may drastically differ from that of Mott insulators with weak SOC (e.g., cuprates) [3,4,14,15]. Of particular interest are d 5 transition metal oxides, such as iridates A 2 IrO 3 (A = Na, Li) [16][17][18], where Na 2 IrO 3 is interpreted as a novel RMI [19] and may also host the quantum spin Hall effect [20,21]. The Kitaev-Heisenberg (KH) model on a honeycomb lattice, which has a rich phase diagram containing unconventional magnetic and Kitaev SL phases [22,23], has been proposed to capture the low-energy properties of A 2 IrO 3 [24,25]. Meanwhile, experiments confirm a longrange zigzag spin order in Na 2 IrO 3 [26][27][28][29], which is a natural GS of the KH model [22]. In addition, there are also studies on the d 4 compound Li 2 RhO 3 , suggesting Li 2 RhO 3 as a possible RMI with a spin-glass GS [30]. Theoretical studies also show that carrier doping into RMIs can induce unconventional superconducting pairings as well as the topological superconductivity (SC) [31][32][33][34][35][36].In fact, the KH model can be generalized to the triangular lattice [37,38]. Similar to the microscopic origin of the honeycomb KH model for A 2 IrO 3 , the triangular KH model can emerge from a class of ABO 2 -type (where A and B are alkali and transition metal ions, respectively) layered compounds [2,3], due to the joint effect of strong SOC, Coulomb interaction, orbital degeneracy, t g 2 5 configuration, and 90°-bonding geometry [...

Using the fluctuation exchange approximation and a three-orbital model, we study the band renormalization, the Fermi surface reconstruction, and the superconducting pairing symmetry in iron-based superconductors. We find that the interorbital spin fluctuations lead to the strong anisotropic band renormalization and the renormalization is orbital dependent. As a result, the topology of Fermi surface displays distinct variation with doping from the electron type to the hole type, which is consistent with the recent experiments. This shows that the Coulomb interactions will have a strong effect on the band renormalization and the topology of the electron Fermi pocket. In addition, the pairing state mediated by the interorbital spin fluctuation is of an extended s-wave symmetry.

Discovery of twin orbital-order ferromagnetic semiconducting phases in VI3-like 2D systems.

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