Abstract
We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brillouin zones. Branched flow appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The strongest branches remain stable indefinitely and may create linear dynamical channels, wherein waves are not confined directly by potential walls as electrons in ordinary wires but rather, indirectly and more subtly by dynamical stability. We term these superwires since they are associated with a superlattice.
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Waves propagating through random media can accumulate in strong branches, intensifying fluctuations and powerful phenomena such as tsunamis. However, branched flow is not restricted to the large scale, and here, we find surprisingly that branched flow is not restricted to random media. We show that quantum waves living in the high Brillouin zones of periodic potentials also branch. Moreover, some of these branches do not decay as in random media but remain robust indefinitely, creating dynamically stable channels that we call superwires. The waves in these stable branches have enough energy to surmount the channel potential and go elsewhere, but classically, nonlinear dynamics keeps them confined within the channel. These results have direct experimental consequences for superlattices and optical systems.
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Daza, A., Heller, E. J., Graf, A. M., & Räsänen, E. (2021). Propagation of waves in high Brillouin zones: Chaotic branched flow and stable superwires. Proceedings of the National Academy of Sciences, 118(40), e2110285118. https://doi.org/10.1073/pnas.2110285118
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