Tunneling in the Brillouin Zone: Theory of Backscattering in Valley Hall Edge Channels

TL;DR

This paper develops a semiclassical theory to understand backscattering in valley Hall edge channels, revealing conditions for suppression of backscattering and the role of domain wall smoothness in topological bosonic systems.

Contribution

It introduces a comprehensive semiclassical framework for tunneling in momentum space, specifically addressing backscattering in valley Hall systems with implications for topological protection.

Findings

Backscattering can be suppressed exponentially with increased domain wall smoothness.

Effective scattering centers depend on local slope and energy of the domain wall.

The theory predicts conditions under which topological protection is maintained.

Abstract

A large set of recent experiments has been exploring topological transport in bosonic systems, e.g. of photons or phonons. In the vast majority, time-reversal symmetry is preserved, and band structures are engineered by a suitable choice of geometry, to produce topologically nontrivial bandgaps in the vicinity of high-symmetry points. However, this leaves open the possibility of large-quasimomentum backscattering, destroying the topological protection. Up to now, it has been unclear what precisely are the conditions where this effect can be sufficiently suppressed. In the present work, we introduce a comprehensive semiclassical theory of tunneling transitions in momentum space, describing backscattering for one of the most important system classes, based on the valley Hall effect. We predict that even for a smooth domain wall effective scattering centres develop at locations determined by both the local slope of the wall and the energy. Moreover, our theory provides a quantitative analysis of the exponential suppression of the overall reflection amplitude with increasing domain wall smoothness.