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

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.

20 pages, 10 figures

References in corpus (28)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Dissipationless Quantum Spin Current at Room Temperature
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Current induced electron spin polarization in strained semiconductors
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Spontaneous Magnon Decays
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Spin-orbital quantum liquid on the honeycomb lattice
• Maximal Rashba-like spin splitting via kinetic energy-driven inversion symmetry breaking
• Superconductivity and Magnetism in Non-centrosymmetric System: Application to CePt_3Si
• A Z${}_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model
• Topological crystalline superconductivity in locally noncentrosymmetric CeRh${}_2$As${}_2$
• Semiclassical ground-state phase diagram and multi-Q phase of a spin-orbit coupled model on triangular lattice
• Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver
• Even-odd parity transition in strongly correlated locally noncentrosymmetric superconductors : An application to CeRh${}_2$As${}_2$
• Perfect flat band with chirality and charge ordering out of strong spin-orbit interaction
• New Microscopic Magnetic Hamiltonian for Exotic Spin Textures in Metals
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Engineering antiferromagnetic skyrmions and antiskyrmions at metallic interfaces
• $\mathrm{SU}(4)$-Symmetric Quantum Spin-Orbital Liquids on Various Lattices
• Magnetism and metal-insulator transitions in the Rashba-Hubbard model
• Sine-square deformed mean-field theory

Cited by in corpus (9)

• Rashba spin-orbit coupling in the square lattice Hubbard model: A truncated-unity functional renormalization group study
• Phase diagram of the quantum spin-1/2 Heisenberg-$\Gamma$ model on a frustrated zigzag chain
• Weyl Semimetallic State in the Rashba-Hubbard Model
• Interaction-driven first-order and higher-order topological superconductivity
• Weyl semimetallic state with antiferromagnetic order in Rashba-Hubbard model
• Weyl semimetallic, Néel, spiral, and vortex states in the Rashba-Hubbard model
• Spin-orbit coupled Hubbard skyrmions
• Transient dynamics and quantum phase diagram for the square lattice Rashba-Hubbard model at arbitrary hole doping
• Effective spin model with anisotropic exchange interactions for the spin-orbit coupled Hubbard model at half-filling