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Abstract

Particlelike scattering states allow for noiseless transport through quantum dots by closely retracing bundles of classical trajectories. We identify such raylike states for electron transport through graphene ribbons. Remarkably, we find that these quasiclassical scattering states can be unambiguously associated with well-defined quantum numbers of the valley degree of freedom specific to graphene. Trigonal warping-i.e., deviations of the band structure from a perfectly isotropic two-dimensional Dirac equation due to the hexagonal lattice structure-results in preferred propagation directions and scattering time delays that depend on the valley the particlelike wave travels in. By implementing a truncated mode basis of Bloch states, we achieve simulations of micrometer-sized quantum dots starting from an atomic-scale tight-binding Hamiltonian.