Helical Fermi Arc in Altermagnetic Weyl Semimetal

TL;DR

This work shows that altermagnetic order, implemented as a $d$-wave altermagnetic mass in a modified Dirac framework, can realize Weyl semimetals with distinctive bulk and surface features not found in conventional magnetic WSMs. A Minimal 3D lattice model reveals Weyl nodes where the Dirac and altermagnetic masses cancel, with 2D slices exhibiting Chern numbers $C(k_z)=+1$ for $|k_z|< frac{ pi}{2}$ and $-1$ for $|k_z|> frac{ pi}{2}$, producing coexisting helical Fermi arcs on the same surface due to opposite-Chern-number blocks. The authors further propose a multilayer architecture of 2D Rashba metals with alternating SOC that yields a $k_z$-dependent mass and a phase diagram featuring trivial, Weyl, and 3D QSH phases, accompanied by robust helical surface states. Together, these results broaden the topological landscape by linking altermagnetic mass terms to novel bulk-boundary phenomena and provide concrete routes for experimental realization of altermagnetic Weyl semimetals.

Abstract

We investigate the topological properties of modified Dirac Hamiltonians with an altermagnetic mass term and reveal a novel mechanism for realizing altermagnetic Weyl semimetals. Unlike the conventional Wilson mass, the altermagnetic mass drives direct transitions between nontrivial Chern phases of opposite sign and fundamentally reshapes the band inversion surface. By extending this framework to three dimensions, we construct a minimal lattice model that hosts pairs of Weyl nodes as well as coexisting helical Fermi arcs with opposite chirality on the same surface, which is a phenomenon not found in conventional magnetic Weyl semimetals. We further propose a practical scheme to realize these phases in multilayer structures of 2-dimensional Rashba metal with engineered $d$-wave altermagnetic order. Our results deepen the theoretical understanding of mass terms in Dirac systems and provide concrete guidelines for the experimental detection and realization of altermagnetic Weyl semimetals.

Figures (5)

• Figure 1: (a) BIS for the Dirac mass and Wilson mass in the continuum model. (b) BIS for the Dirac mass and altermagnetic mass in the continuum model. (c) BIS for the Dirac mass and Wilson mass in the lattice model, with $m_0=-1$ and $J=1$; color indicates the $d_{z}$ component. (d) BIS for the Dirac mass and altermagnetic mass in the lattice model, with $m_0=-1$ and $J=1$. (e) Chern number as a function of Dirac mass $m_0$ for altermagnetic mass (blue line) and Wilson mass (red line); the three points marked c, d, and f correspond to different $d_{z}$ distributions in the Brillouin zone in the panels (c, d, and f). (f) BIS for the Dirac mass and altermagnetic mass in the lattice model, with $m_0=1$ and $J=1$.
• Figure 2: (a1– a5) Slab energy spectra as a function of $k_{z}$ in the Weyl semimetal phase, with eigenstates color-coded according to their average position $\langle x\rangle$ to distinguish surface and bulk states. (b) The corresponding Chern number $C(k_{z})$ for each fixed $k_{z}$ slice. (c) Distribution of Weyl nodes in the Brillouin zone, with Fermi arcs connecting pairs of nodes. (d) Berry curvature distribution in the Brillouin zone, highlighting regions of concentrated topological charge.
• Figure 3: (a) Schematic illustration of the proposed altermagnetic multilayer: two-dimensional metallic layers with $d$-wave altermagnetic order are stacked along $z$, and adjacent layers carry Rashba spin– orbit couplings of opposite sign $(+\lambda,\,-\lambda)$, as shown by the large green arrows. Thin insulating spacers suppress further-neighbour hopping, while intra-cell hybridization $\Delta_{S}$ and inter-cell tunnelling $\Delta_{D}$ are indicated. (b) Topological phase diagram as a function of the altermagnetic mass $J$ and tunneling parameters $\Delta_{S}$, $\Delta_{D}$. The diagram highlights the regions corresponding to the trivial insulator, Weyl semimetal, and QSH phases. The three points (labeled I, II, III) indicate parameter sets used for the subsequent bulk and edge calculations, with specific values $(\Delta_S, \Delta_D) = (0.5, 0.5)$ for I, (1, 0.5) for II, and (1.5, 0.5) for III. In all calculations, we set $t=0.1$, $\lambda=0.5$, and $J=0.5$.
• Figure 4: (a– c) Fermi surface distributions for three representative parameter sets, marked by points I, II, and III in Fig. \ref{['fig:3']}(b). (d1– d5) Slab spectra as a function of $k_{z}$ in the Weyl semimetal phase with $\Delta D=0.5$ and $\Delta S=1$, with eigenstates color-coded by their average position $\langle x\rangle$. (e) The corresponding Chern number $C(k_{z})$, which exhibits a jump at the Weyl nodes. (f1– f5) Slab spectra as a function of $k_{z}$ in the QSH phase with $\Delta D=0.5$ and $\Delta S=0.2$, again color-coded by average position. (g) The corresponding Chern number $C(k_{z})$, remaining constant throughout, consistent with robust QSH edge states and the absence of Weyl nodes.
• Figure 5: (a,b) Momentum-space textures of $\mathbf{d}(\mathbf{k})=(d_x,d_y,d_z)$ for the hexagonal-lattice model with Dirac masses $m_0=\pm1$, $v_F=1$, and $J=1$. The band-inversion surfaces defined by $d_z(\mathbf{k})=0$ enclose the $K$ and $K^{\prime}$ valleys for opposite mass signs