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

TL;DR

This paper theoretically demonstrates that a specific noncoplanar spin order on a cubic lattice induces three-dimensional Dirac electrons, which can be transformed into Weyl semimetals under magnetic fields, with implications for topological materials.

Contribution

It reveals that a triple-Q noncoplanar order on a cubic lattice induces 3D Dirac electrons and explores their stability in correlated electron models, connecting magnetic order to topological electronic states.

Findings

Triple-Q order induces 3D massless Dirac electrons.

External magnetic field splits Dirac into Weyl nodes, creating a Weyl semimetal.

Dirac electrons produce surface Fermi arcs connecting Dirac points.

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 \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, similarly to Weyl semimetals.