# Non-trivial topological valence bands of common diamond and zinc-blende semiconductors

## TL;DR

This study reveals unexpected topological properties in the valence bands of common diamond and zinc-blende semiconductors like InSb and GaAs, combining theoretical analysis and experimental validation to uncover topological surface states.

## Contribution

The paper demonstrates for the first time that the valence bands of these semiconductors have non-trivial topological characteristics induced by spin-orbit coupling, supported by ab initio calculations and experiments.

## Key findings

- Topological surface states found below Fermi energy in InSb and GaAs.
- Spin-orbit split-off bands exhibit strong topologically non-trivial behavior.
- Experimental evidence from soft X-ray ARPES confirms theoretical predictions.

## Abstract

The diamond and zinc-blende semiconductors are well-known and have been widely studied for decades. Yet, their electronic structure still surprises with unexpected topological properties of the valence bands. In this joint theoretical and experimental investigation we demonstrate for the benchmark compounds InSb and GaAs that the electronic structure features topological surface states below the Fermi energy. Our parity analysis shows that the spin-orbit split-off band near the valence band maximum exhibits a strong topologically non-trivial behavior characterized by the $\mathcal{Z}_2$ invariants $(1;000)$. The non-trivial character emerges instantaneously with non-zero spin-orbit coupling, in contrast to the conventional topological phase transition mechanism. \textit{Ab initio}-based tight-binding calculations resolve topological surface states in the occupied electronic structure of InSb and GaAs, further confirmed experimentally by soft X-ray angle-resolved photoemission from both materials. Our findings are valid for all other materials whose valence bands are adiabatically linked to those of InSb, i.e., many diamond and zinc-blende semiconductors, as well as other related materials, such as half-Heusler compounds.