Chiral-Angle-Controlled Altermagnetic Spin Splitting in Nanotubes

Altermagnets exhibit momentum-dependent spin splitting despite having zero net magnetization. Here, we show that rolling a two-dimensional (2D) $d$-wave altermagnet into a nanotube transforms this momentum-dependent spin splitting into chiral-angle-controlled one-dimensional (1D) spin splitting through dimensional projection. Using a minimal tight-binding model and first-principles calculations, we demonstrate that the nanotube spin splitting follows a characteristic $\cos(2\theta)$ dependence, vanishing for nodal orientations and reaching extrema for antinodal orientations. The mechanism remains robust across a broad class of nanotubes derived from 2D altermagnets. Our results establish dimensional projection as a general route for transferring momentum-dependent altermagnetic spin splitting into 1D systems and provide a framework for engineering spin-split quantum states in low-dimensional magnetic materials.