Quasi-1D Planar Magnetic Topological Heterostructure

Abstract

We theoretically introduce a quasi-1D magnetic heterostructure of alternating 2D topological and normal insulator strips. Its low-energy physics is governed by a hybrid Hamiltonian intertwining the Su-Schrieffer-Heeger and Shockley models, with spin-momentum locking and local Zeeman splitting. Symmetry analysis places it in class AIII, characterized by chiral symmetry and a $\mathbb{Z}$ topological invariant. Computing the winding number from the block-off-diagonal structure of the Hamiltonian reveals topological phases characterized by invariants $\nu = 0$, $1$, and $2$. Furthermore, a single magnetic defect acts as a sensitive local probe, whose in-gap spectrum provides a spectroscopic fingerprint to distinguish topological phases. Extending the platform to a multilayer geometry uncovers a nonsymmorphic projective symmetry that gives rise to M\"obius band topology, with the Brillouin zone compactifying into a Klein bottle. Our work establishes a platform for higher-order topology via heterostructure design and magnetic patterning.