Texture-induced low-dimensional topology in class D spinful models

You-Xun Zhang^1*, Chang-Tse Hsieh¹

¹Department of Physics, National Taiwan University, Taipei, Taiwan

* Presenter:You-Xun Zhang, email:jim901024@gmail.com

We investigate one-dimensional topological superconductors (TSCs) with real-space parameter
textures. Considering models with various forms of superconducting pairing, we show that such
textures can induce additional topological characteristics beyond the conventional one protected by
particle-hole symmetry in class D systems. The topology of the texture itself plays a crucial role
in extending the topological classification. For instance, an S1-valued magnetic or spin texture can
simultaneously contribute to the one-dimensional bulk topology of class D and to an additional zero
dimensional topological structure within the same class. Since the presence of textures invalidates
the standard momentum-space classification, we introduce a real-space Z2 topological invariant
that characterizes textured TSCs. We compute this invariant analytically and numerically for
representative texture profiles, and we develop a continuum and defect-based formulation applicable
to slowly varying textures. We further clarify the origin of this invariant in specific parameter
regimes, showing how texture-induced topology links bulk and defect classifications and enables
new classes of topological superconducting phases in inhomogeneous systems.

Keywords: Spin texture, Topological phase, Fermion parity, Pfaffian, Chern number