# Double Band Inversion in $ \alpha $-Sn: Appearance of Topological Surface States and the Role of Orbital Composition

## TL;DR

This study reveals a new topological surface state in strained b5-Sn, demonstrating the role of orbital composition in protecting topological states and combining experimental and theoretical approaches.

## Contribution

It uncovers a novel topological surface state within the bulk band gap of strained b5-Sn and explains its orbital protection mechanism through combined experimental and ab initio calculations.

## Key findings

- Discovery of a new topological surface state within the bulk band gap.
- Orbital composition differences explain the localization and protection of topological states.
- Experimental and theoretical results are in strong agreement.

## Abstract

The electronic structure of \graySn(001) thin films strained compressively in-plane was studied both experimentally and theoretically. A new topological surface state (TSS) located entirely within the gapless projected bulk bands is revealed by \textit{ab initio}-based tight-binding calculations as well as directly accessed by soft X-ray angle-resolved photoemission. The topological character of this state, which is a surface resonance, is confirmed by unravelling the band inversion and by calculating the topological invariants. In agreement with experiment, electronic structure calculations show the maximum density of states in the subsurface region, while the already established TSS near the Fermi level is strongly localized at the surface. Such varied behavior is explained by the differences in orbital composition between the specific TSS and its associated bulk states, respectively. This provides an orbital protection mechanism for topological states against mixing with the background of bulk bands.