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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 bandstructures are engineered by a suitable choice of geometry, to produce topologically nontrivialbandgaps in the vicinity of high-symmetry points. However, this leaves open the possibility oflarge-quasimomentum backscattering, destroying the topological protection. Up to now, it has beenunclear what precisely are the conditions where this effect can be sufficiently suppressed. In thepresent work, we introduce a comprehensive semiclassical theory of tunneling transitions in momen-tum space, describing backscattering for one of the most important system classes, based on thevalley Hall effect. We predict that even for a smooth domain wall effective scattering centres developat locations determined by both the local slope of the wall and the energy. Moreover, our theoryprovides a quantitative analysis of the exponential suppression of the overall reflection amplitudewith increasing domain wall smoothness.