Majoranas with a twist: Tunable Majorana zero modes in altermagnetic heterostructures

TL;DR

This work demonstrates that altermagnetic order enables orientation-dependent spin splitting in a proximitized semiconductor wire, making the topological superconducting phase tunable by rotating or bending the wire rather than by external fields. Through symmetry arguments and a Schrieffer–Wolff transformation, the authors derive an angle-dependent effective Hamiltonian with an induced altermagnetic term $\tilde{J}$, establish gap-closing conditions for $d$-, $g$-, and $i$-wave altermagnets, and show that curved geometries can host Majorana zero modes at phase boundaries without additional tuning. The findings suggest a versatile platform for Majorana physics, potentially aided by altermagnetic domain engineering, with practical routes given current experimental progress on altermagnets like MnTe and CrSb. The work calls for further first-principles studies and exploration of strain and non-collinear altermagnetic configurations to enhance and generalize the proposed scheme.

Abstract

Altermagnetism provides new routes to realize Majorana zero modes with vanishing net magnetization. We consider a recently proposed heterostructure consisting of a semiconducting wire on top of an altermagnet and with proximity-induced superconductivity. We demonstrate that rotating the wire serves as a tuning knob to induce the topological phase. For $d$-, $g$- and $i$-wave altermagnetic pairing, we derive angle-dependent topological gap-closing conditions. We derive symmetry constraints on angles where the induced altermagnetism must vanish, which we verify by explicit models. Our results imply that a bent or curved wire realizes a spatially-dependent topological invariant with Majorana zero modes pinned to positions where the topological invariant changes. This provides a new experimental set-up whereby a single wire can host both topologically trivial and nontrivial regimes without $in$ $situ$ tuning.

Figures (3)

• Figure 1: Proposed setups consisting of superconducting wires (a) rotated or (b) bent on top of a ($d$-wave) altermagnet, with schematic top-down views in the insets. The red and blue lobes indicate the sign of the underlying altermagnetic order. Green and black segments correspond to topological and trivial regimes respectively, with localized Majoranas at their interfaces (stars in the insets). In (a), straight wires rotated at different angles relative to the underlying altermagnet reveal that beyond a critical angle (magenta line in inset), a topological phase transition occurs. In (b), a bent wire exhibits a spatially dependent topological order parameter due to its "continuous rotation".
• Figure 2: Effective altermagnetic coupling $\Tilde{J}(k,\theta)$ vs angle at $k=0$ for a) $d$-wave, b) $g$-wave and c) $i$-wave altermagnetic order. The insets show the underlying altermagnetic order, with (a) indicating the real space angle of the wire relative to the underlying altermagnetic anisotropy.
• Figure 3: Polar plots of topological phase diagrams for a) $d$-wave, b) $g$-wave and c) $i$-wave proximity induced altermagnetism. Radial coordinate corresponds to $J$ from the underlying altermagnet. Plots are made for $\Tilde{\mu}_{W,R}=0.15,$$\Delta=0.1$ and $\frac{t^2_{I,i}}{\Delta \mu^2}=\frac{1}{25}$ in units of the effective mass with $m_W=1$.