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 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 $\vec{k}$ are equivalent to the ones of spin down at $\vec{k}+\vec{Q}$ with so-called the \textit{shifting wave vector} $\vec{Q}$. Thus, the system stabilizes 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 $\vec{Q}$. We first show the condition for existence of the \textit{shifting wave vector} in general lattice model and emergent $SU(2)$ symmetry in the spin orbit coupled system. Then, we exemplify this in square lattice at half filling and discuss the insulating phase with (non-) coplanar spin density wave and charge order. Our study emphasizes possible new types of two dimensional magnetic materials and can be applicable to various van-der Waals materials and their heterostructures with the control of electric field, strain and pressure.

arXiv comment7 pages, 8 figures

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Cited by in corpus (3)

• Phase diagram of the square lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling
• Sine-square deformed mean-field theory
• Analytically solvable model to the spin Hall effect with Rashba and Dresselhaus spin-orbit couplings