Spin-helix-driven insulating phase in two-dimensional lattice

Abstract

Motivated by emergent SU(2) symmetry in the spin-orbit-coupled system, we study the spin-helix-driven insulating phase in a two-dimensional lattice. When both Rashba and Dresselhaus spin-orbit couplings are present, the perfect Fermi-surface nesting occurs at a special condition depending on the lattice geometry. In this case, the energies of spin up at any wave vector →k are equivalent to the ones of spin down at →k+→Q with the shifting wave vector →Q. Thus, the system stabilizes the magnetic insulator with spiral-like magnetic ordering even in the presence of tiny electron-electron interaction where the magnetic ordering wave vector is proportional to →Q. We first show the condition for the existence of the shifting wave vector in a general lattice model and emergent SU(2) symmetry in the spin-orbit-coupled system. Then, we exemplify this in a square lattice at half filling and discuss the insulating phase with (non)coplanar spin density wave and charge order. Our study emphasizes different possible types of two-dimensional magnetic materials that can be applicable to various van der Waals materials and their heterostructures with the control of electric field, strain, and pressure.