Weyl semimetallic state with antiferromagnetic order in Rashba-Hubbard model

TL;DR

This work investigates how Rashba spin-orbit coupling and on-site electronic repulsion in a one-orbital Rashba-Hubbard model give rise to a topological, antiferromagnetically ordered metallic state. Using static Hartree-Fock mean-field theory, the authors map the phase diagram in the $U$-$λ$ plane and identify a Weyl semimetallic antiferromagnet (WSM-AFM) phase that sits between a Rashba metal and an AFM insulator; this phase features two pairs of Weyl points whose locations and topological winding numbers are determined by the exchange field $Δ$ and SOC strength $λ$, with $|Δ|\le 2λ$ as a key condition. They analyze edge states and compute Berry windings, demonstrating robust topological character, and they examine spin-resolved quasiparticle interference to reveal the spin texture near the Weyl nodes. The results show that magnetic order can coexist with topological semimetallic states in systems with Rashba SOC, offering experimentally accessible signatures via spin-resolved ARPES and STM/QPI. Overall, the paper advances understanding of how correlations and SOC stabilize topological phases and provides concrete predictions for Weyl points, edge modes, and spin textures in a paradigmatic lattice model.

Abstract

We study the phase diagram of Rashba-Hubbard model by employing the Hartree-Fock meanfield theory, and thereby establish the existence of an antiferromagnetically ordered Weyl semimetallic state with in-plane magnetic moments. This phase is found to be sandwiched in between the antiferromagnetic insulator and Rashba metal in the interaction vs spin-orbit coupling phase diagram. The antiferromagnetically-ordered topological semimetallic state exists in the presence of combined time-reversal and inversion symmetry though individually both are broken. The study of the static magnetic susceptibility indicates the robustness of the antiferromagnetic order within a realistic range of interaction and spin-orbit coupling parameters. In addition to the edge states associated with the Weyl points, we also investigate the spin-resolved quasiparticle interference, which provides important insight into the possible spin texture of the bands especially in the vicinity of Weyl points.

Figures (11)

• Figure 1: Various components of the static spin susceptibility in the whole Brillouin zone $(a$-$f)$ and also along the high-symmetry directions $(g$-$h)$ showing peaks for $\lambda = 0.3$ and $0.6$.
• Figure 2: Fermi-surfaces with one of the prominent nesting vectors ${\bf Q} = (\pi,\pi)$ at half-filling for (a) $\lambda = 0.4$ and (b) $\lambda = 0.8$, where the range of both $k_x$ and $k_y$ is $[-\pi,\pi]$ .
• Figure 3: Phase-diagram showing various phases for the correlation strengths $0 \le U \le 8$ and Rashba SOC strength $0 \le \lambda \le 1$. Three different phases including AFM-I (antiferromagnetic insulator), WSM-AFM (Weyl semimetallic antiferromagnet), and RM (Rashbha metal).
• Figure 4: DOS corresponding to the three different phases, RM, AFM-I, and WSM-AFM. For $U = 0$ and $\lambda = 0.5$, a significant DOS is obtained at Fermi level characteristic of a metallic system. In case of $U = 5$ and $\lambda = 0.5$, the DOS is gapped at the Fermi level indicating the insulating behavior of the system. Upon increasing SOC further so that $\lambda = 1$, the DOS is zero at the Fermi level, whereas it does not vanish in the immediate vicinity, indicating a semimetallic state.
• Figure 5: Electronic dispersions are plotted for different sets of $U$ and $\lambda$ values. They correspond to the three phases (a) RM, (b) WSM-AFM, and (c) AFM-I.