Phase diagram of the square lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling

TL;DR

This paper maps the phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling, revealing incommensurate SDW phases and various magnetic states driven by Fermi surface nesting and SOC effects.

Contribution

It introduces a comprehensive multi-method approach to uncover complex magnetic phases in the Hubbard model with Rashba SOC, including previously overlooked incommensurate SDW states.

Findings

Identification of incommensurate SDW phases with long spatial periods.

Discovery of phase transitions driven by Fermi surface nesting.

Observation of spiral, stripe, and vortex phases at large SOC.

Abstract

We clarify the ground state phase diagram of the half-filled square-lattice Hubbard model with Rashba spin-orbit coupling (SOC) characterized by the spin-split energy bands due to broken inversion symmetry. Although the Rashba metals and insulating magnets have been studied well, the intermediate interaction strength of the system remained elusive due to the lack of appropriate theoretical tools to unbiasedly describe the large-scale magnetic structures. We complementarily apply four different methods; sine square deformed mean-field theory, random phase approximation, Luttinger-Tisza method, and density matrix embedding theory, and succeed in capturing the incommensurate spin density-wave (SDW) phases with very long spatial periods which were previously overlooked. The transition to the SDW phases from the metallic phase is driven by an unprecedented instability that nests the two parts of the Fermi surface carrying opposite spins. For large SOC, the spiral, stipe, and vortex phases are obtained, when the four Dirac points exist near the Fermi level and their whole linear dispersions nest by a wavelength $\pi$, opening a band gap. These two types of transition provide Fermiology that distinguishes the antisymmetric SOC systems, generating a variety of magnetic phases that start from the relatively weak correlation regime and continue to the strongly interacting limit.