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From the scattering of semicoherent-state wavepackets at high magnetic field,we derive analytically the transmission coefficient of electrons in graphene inthe quantum Hall regime through a smooth constriction described by a quadraticsaddle-point electrostatic potential. We find anomalous half-quantizedconductance steps that are rounded by a backscattering amplitude related to thecurvature of the potential. Furthermore, the conductance in graphene breaksparticle-hole symmetry in cases where the saddle-point potential is itselfasymmetric in space. These results have implications both for theinterpretation of split-gate transport experiments, and for the derivation ofquantum percolation models for graphene.

Transmission coefficient through a saddle-point electrostatic potential for graphene in the quantum Hall regime