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arXiv:2208.09902 · Physical review. B./Physical review. B

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

Masataka Kawano, Chisa Hotta

Published Jan 17, 2023• 16 citations
arXivHTMLPDF

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 $\ensuremath{\pi}$, 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.

DOI
10.1103/physrevb.107.045123

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We investigate the metal-insulator transition (MIT) and phase diagram of the half-filled Fermi Hubbard model with Rashba-type spin-orbit coupling (SOC) on a square optical lattice. The interplay between the atomic interactions and SOC results in distinctive features of the MIT. Significantly, in addition to the diverse spin ordered phases, a nonmagnetic insulating phase emerges in a considerably large regime of parameters near the Mott transition. This phase has a finite single-particle gap but vanishing magnetization and spin correlation exhibits a power-law scaling, suggesting a potential algebraic spin-liquid ground state. These results are confirmed by the non-perturbative cluster dynamical mean-field theory.
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Abstract Based on the two-dimensional (2D) attractive Fermi-Hubbard model with Rashba spin–orbit coupling (SOC), the SOC strength and Zeeman field dependences of the phase diagram are investigated by calculating the pairing gap self-consistently. The results reveal that the phase transition from the BCS superfluid to the topological superfluid happens under proper Zeeman field strength and SOC strength. In particular, in contrast to the BCS superfluid decreasing monotonically as the SOC strength increasing, the topological superfluid region shows a dome with the SOC strength increasing. An optimal region in the phase diagram to find the topological superfluid can be found, which is important to realize the topological superfluid in optical lattice experimentally. Then we obtain the change of both band structure and density of states (DOSs) during the topological phase transition, and explain the four peaks of DOS in the topological superfluid by the topology change of the low-energy branch of quasiparticle energy spectra. Moreover, the topological superfluid can be suppressed by the doping concentration.
In this work, we investigate the impact of Rashba spin-orbit coupling (RSOC) on the formation of charge-density wave (CDW) and superconducting (SC) phases in the Holstein model on a half-filled square lattice. Using unbiased finite-temperature Quantum Monte Carlo simulations, we go beyond mean-field approaches to determine the ground state order parameter as a function of RSOC and phonon frequency. Our results reveal that the Rashba metal is unstable due to particle-hole instabilities, favoring the emergence of a CDW phase for any RSOC value. In the limit of a pure Rashba hopping, the model exhibits a distinct behavior with the appearance of four Weyl cones at half-filling, where quantum phase transitions are expected to occur at strong interactions. Indeed, a quantum phase transition, belonging to the Gross-Neveu Ising universality class between a semi-metal and CDW emerges at finite phonon frequency dependent coupling λcλ_cλc​. In the antiadiabatic limit we observe an enhanced symmetry in the infrared that unifies SC and CDW orders. These results advance our understanding of competing CDW and SC phases in systems with spin-orbit coupling, providing insights that may help clarify the behavior of related materials.