Imagine a crystal where an electron, having completed a full loop in momentum space, returns not to its original state but to its mirror reflection. This is not abstract geometry, but the physical reality of the band structure predicted in our new work on heterostructures based on topological insulators.

In the paper, we propose an effective model of a layered system consisting of alternating quasi-one-dimensional strips of topological and normal insulators. The key feature of this construction is the presence of a specific non-symmorphic projective symmetry. We demonstrate that this symmetry forces the energy bands to behave as a topological Möbius surface (and in the full three-dimensional picture, as a Klein bottle).

What does this offer condensed matter physics? First, the Möbius band topology guarantees the emergence of symmetry-protected Dirac points in both gapped and gapless phases. Second, and more intriguingly, when introducing controlled dissipative effects (non-Hermiticity), this geometry gives rise to a topologically protected non-Hermitian skin effect. Unlike standard mechanisms, the localization of states at the sample edges here is dictated by the Möbius connectivity of the bands—electrons become "trapped" at the surface for fundamental symmetry reasons. This opens new avenues for controlling wave packets in real devices.

This result will be of broad interest to researchers working on topological phases, quantum geometry, and open quantum systems.

Figure 1. Schematic of the proposed heterostructure. (a) 3D visualization: a stack of quasi-1D strips shifted (step-stacked) relative to each other. Each strip consists of alternating ribbons of 2D topological (TI) and normal (NI) insulators. Intralayer ($\Delta _1, \Delta _2$) and interlayer ($\Delta $) hopping integrals between edge modes (marked with A and B) are shown (b) Side-view equivalent, illustrating the 2D periodicity. The system possesses non-symmorphic projective translation symmetry – reflection $M_x $ and a half-period shift along Z (in the basis (1,2)). Translational invariance along X is broken by dimerization (sublattices A and B). (c) Difference between mirror reflection of chiral and trivial dimers.

Z.Z. Alisultanov
JETP Letters 123, issue 9 (2026)