# Role of helical edge modes in the chiral quantum anomalous Hall state

## TL;DR

This paper investigates whether the topological protection of quantum spin Hall edge modes carries over during their evolution into quantum anomalous Hall edge modes, especially under disorder and scattering, challenging previous experimental interpretations.

## Contribution

It explores the conditions under which QAH edge modes remain topologically protected, questioning the assumption that QSH protection always transfers during the evolution process.

## Key findings

- Transport via trivial QAH edge modes leads to Hall resistance quantization.
- Topological QAH edge modes may not always be responsible for observed signatures.
- Reinterpretation of experiments claiming chiral QAH edge modes is suggested.

## Abstract

Although indications are that a single chiral quantum anomalous Hall(QAH) edge mode might have been experimentally detected. There have been very many recent experiments which conjecture that a single chiral QAH edge mode always materializes along with a pair of quasi-helical quantum spin Hall (QSH) edge modes. The reason for this seems to lie in the origin of QAH edge modes. These evolve from QSH edge modes via suppression of one of the spin edge modes by application of a ferromagnet or magnetic impurity. In this work we deal with a substantial 'What If ?' question- in case the QSH edge modes, from which these QAH edge modes evolve, are not topologically protected then the QAH edge modes wont be topologically protected too and thus unfit for use in any applications. Further, as a corollary one can also ask if the topological protection of QSH edge modes does not carry over during the evolution process to QAH edge modes then again our 'What if?' scenario becomes apparent. The "how" of the resolution of this 'What if?' conundrum is the main objective of our work. We show in similar set-ups affected by disorder and inelastic scattering, transport via trivial QAH edge mode leads to quantization of Hall resistance and not that via topological QAH edge modes. This perhaps begs a substantial reinterpretation of those experiments which purported to find signatures of chiral(topological) QAH edge modes albeit in conjunction with quasi helical QSH edge modes.