Real and momentum space analysis of topological phases in 2D d-wave altermagnets

TL;DR

This work develops a real- and momentum-space framework to study topological phases in 2D $d$-wave altermagnets, revealing a topological phase transition at the critical intra-sublattice hopping $t_a^C$. By analyzing Dirac nodal points, Berry curvature, and pseudospin textures, it shows a transition from a gapped altermagnetic insulator to a nodal semimetal with Dirac points, and eventually to a topological phase with enhanced spin polarization and edge states. The authors connect bulk topology to edge phenomena via fidelity-susceptibility and inverse participation ratio, and propose an energy-gap engineering strategy in ultranarrow nanoribbons to realize a topological altermagnetic field-effect transistor (FET) with spin-polarized, gate-tunable transport. Collectively, the study provides a theoretical and information-theoretic framework for edgetronics in altermagnets, with potential applications in high-speed spintronics and spin-splitter logic devices.

Abstract

Altermagnetism has recently emerged as a third fundamental branch of magnetism, combining the vanishing net magnetization of antiferromagnets with the high-momentum-dependent spin splitting of ferromagnets. This study provides a comprehensive real- and momentum-space analysis of topological phases in two-dimensional d-wave altermagnets. By employing a tight-binding Hamiltonian, we characterize the topological phase transition occurring at a critical intra-sublattice hopping strength ($t_a^C$). We examine the emergence of Dirac nodal points and the resulting Berry curvature singularities, supported by a visual analysis of pseudospin texture winding. Crucially, we analize spin splitting, effective altermagnetic strength, and investigate the transport implications of these phases, uncovering giant conductivity anisotropy and spin-dependent "steering" effects driven by group velocity distribution across the Fermi surface. Beyond bulk properties, we analyze the edge state topology in ribbon geometries through the lens of information-theoretic markers like fidelity-susceptibility and inverse participation ratio, offering an alternative to traditional Chern number calculations. Our results demonstrate that the hybridization of edge states in ultra-narrow nanoribbons opens a controllable energy gap, a feature we exploit to propose a novel topological altermagnetic field-effect transistor design where ballistic and spatially spin-polarized transport can be electrostatically gated. This work establishes a theoretical and information-theoretic framework for "edgetronics" in altermagnetic materials, paving the way for next-generation, high-speed spintronic and "spin-splitter" logic devices and architectures.

Figures (14)

• Figure 1: Real-space representation of 2D $\mathrm{d}_{x^2-y^2}$-- and $\mathrm{d}_{xy}$--wave AM lattices and their BZs.
• Figure 2: Berry curvature (top row) and pseudo-spin (pseudo-Zeeman field) texture (bottom row) as a function of $\bm{k}=(k_x,k_y)$ for spin $s=-1$ in the trivial phase $t_a<J/4$ (left) and the topological phase $t_a>J/4$ (right). Dirac points $\bm{k}_D=(\pm k_D,\pi)$ for $t_a>J/4$ are marked with filled red dots in both contour and vector plots.
• Figure 3: Left: Energy dispersion as a function of $k_x$ for 20 values of $k_y$. Right: Spin splitting along the trajectory $\Gamma\to X\to M\to \Gamma$ in BZ. Hamiltonian parameters $J=1=t, t_a=0.5>t_a^c=J/4$
• Figure 4: $P_\mathrm{eff}$ versus $t_a$ for the Fermi energies $E_F=n\sqrt{J^2+16t^2}/4, n=0,1,2,3,4$ (from thikest to thinest curves). The critical point $t_a^C=J/4$ is marked with a vertical gridline. Hamiltonian parameters: $J=1=t$ and broadening $\eta=0.1$ meV.
• Figure 5: Group velocity distribution accros the FS ($E_F=\pm 2$ meV), for conduction $(+)$ and valence $(-)$ bands and spin up (red) and down (blue)). Hamiltonian parameters: $J=1=t, t_a=0.2$ meV