3D Dirac Electrons on a Cubic Lattice with Noncoplanar Multiple-Q Order

Abstract

Noncollinear and noncoplanar spin textures in solids manifest themselves not only in their peculiar magnetism but also in unusual electronic and transport properties. We here report our theoretical studies of a noncoplanar order on a simple cubic lattice and its influence on the electronic structure. We show that a four-sublattice triple-Q order induces three-dimensional massless Dirac electrons at commensurate electron fillings. The Dirac state is doubly degenerate, while it splits into a pair of Weyl nodes by lifting the degeneracy by an external magnetic field; the system is turned into a Weyl semimetal in applied field. In addition, we point out the triple-Q Hamiltonian in the strong coupling limit is equivalent to the 3D π-flux model relevant to an AIII topological insulator. We examine the stability of such a triple-Q order in two fundamental models for correlated electron systems: a Kondo lattice model with classical localized spins and a periodic Anderson model. For the Kondo lattice model, performing a variational calculation and Monte Carlo simulation, we show that the triple-Q order is widely stabilized around 1/4 filling. For the periodic Anderson model, we also show the stability of the same triple-Q state by using the mean-field approximation. For both models, the triple-Q order is widely stabilized via the couplings between conduction electrons and localized electrons even without any explicit competing magnetic interactions and geometrical frustration. We also show that the Dirac electrons induce peculiar surface states: Fermi "arcs" connecting the projected Dirac points, similarly to Weyl semimetals.

10 pages, 7 figures

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• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Dirac semimetal in three dimensions
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Existence of bulk chiral fermions and crystal symmetry
• Hidden Multiple-spin Interactions as an Origin of Spin Scalar Chiral Order in Frustrated Kondo Lattice Models
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Cited by in corpus (25)

• Topological spin crystals by itinerant frustration
• Multiple-Q Instability by (d-2)-dimensional Connections of Fermi Surfaces
• Néel- and Bloch-Type Magnetic Vortices in Rashba Metals
• Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
• Effect of magnetic anisotropy on Skyrmions with a high topological number in itinerant magnets
• Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities
• Novel magnetic orderings in the kagome Kondo-lattice model
• Incommensurate spiral order from double exchange interactions
• Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions
• Widely-sweeping magnetic field-temperature phase diagrams for skyrmion-hosting centrosymmetric tetragonal magnets
• Engineering chiral density waves and topological band structures by multiple-$Q$ superpositions of collinear up-up-down-down orders
• Itinerancy-dependent non-collinear spin textures in SrFeO3, CaFeO3, and CaFeO3/SrFeO3 heterostructures probed via resonant x-ray scattering
• Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet
• Spin Conductivity Based on Magnetic Toroidal Quadrupole Hidden in Antiferromagnets
• Topological semimetal-to-insulator phase transition between noncollinear and noncoplanar multiple-Q states on a square-to-triangular lattice
• Charge density waves in multiple-$Q$ spin states
• Nonreciprocal Transport in Noncoplanar Magnetic Systems without Spin-Orbit Coupling, Net Scalar Chirality, or Magnetization
• Magnetic phase diagram slightly below the saturation field in the stacked $J_1$-$J_2$ model in the square lattice with the $J_{\text{C}}$ interlayer coupling
• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Low-temperature magnetic properties of the Kondo lattice model in one dimension
• Anisotropic spin model and multiple-$Q$ states in cubic systems
• Phase Diagram of the Shastry-Sutherland Kondo Lattice Model with Classical Localized Spins: A Variational Calculation Study
• Topological Hall effect in the Shastry-Sutherland lattice
• Theory of magnetic vortex crystals induced by electric dipole interactions
• Double-$Q$ and quadruple-$Q$ instabilities at low-symmetric ordering wave vectors under tetragonal symmetry