Branched Flow and Stable Superwires in Periodic Two-Dimensional Systems

Branched flow is a common phenomenon in wave dynamics, where deflections of particles, rays or waves due to random fluctuations in the surrounding medium eventually lead to a chaotic arborescent pattern. Branched flow has been reported in a remarkable variety of physical systems covering, e.g., pulsar-generated microwaves, ocean waves, beams of light and two-dimensional (2D) electron gas [1,2].

Here we report unexpected branched flow in electronic wave-packet dynamics of 2D periodic lattices without any randomized disorder [2]. The branching appears at wavelengths shorter than the typical length scale of the ordered periodic structure and for energies above the potential barrier. The branching is qualitatively similar in classical and quantum description. The strongest branches remain stable indefinitely and may create linear dynamical channels. In these channels the waves are not confined directly by potential walls as electrons in ordinary wires but rather, indirectly and more subtly by dynamical stability. We discuss the relevance of these "superwires" in 2D materials, especially in moiré superlattices, where the wavelengths are typically small compared to the lattice constant - thus creating an ideal system for branched flow.

[1] For a review, see E. J. Heller, R. Fleischmann, and T. Kramer, Physics Today 74, 12, 44 (2021).

[2] A. Daza, Eric J. Heller, A. M. Graf, and E. Rasanen, Proc. Nat. Acad. Sci. 118 (40), e2110285118 (2021).