Three-dimensional Dirac electrons on a cubic lattice with noncoplanar multiple-Qorder

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 an applied field. In addition, we point out the triple-$Q$ Hamiltonian in the strong coupling limit is equivalent to the 3D $\ensuremath{\pi}$-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, similar to Weyl semimetals.