# Su-Schrieffer-Hegger (SSH) model with non-orientable bulk: Union of topology and flat bands in one dimension

## TL;DR

This study explores a modified SSH model with a non-orientable bulk, revealing preserved topology, flat bands at the Fermi level, and a unique combination of flat bands with non-trivial topology in one dimension.

## Contribution

Introduces a SSH model with a non-orientable bulk, demonstrating the coexistence of flat bands and topological properties in one dimension.

## Key findings

- Topology preserved with non-orientable bulk
- Presence of doubly degenerate flat bands at Fermi level
- System exhibits metallic behavior with localized electrons

## Abstract

In this letter we summarise our study of Su-Schrieffer-Hegger(SSH) model with a one dimensional non-orientable manifold as bulk. For this purpose a SSH model with any bulk (SAB) is introduced. We observe the following: (1) The topology of the SSH model is preserved even with a non-orientable bulk, (2) The appearance of a doubly degenerate flat band exactly at the Fermi level, (3) At half filling the band structure is metallic due to the complete overlap of valence and conduction band but the electrons will be localised because the bands are flat and (4) This system is unique because it has flat bands and at the same time is topologically non-trivial.