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.

We report unexpected classical and quantum dynamics of a wave propagating in a periodic potential in high Brilloiun 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.

The development of electrochemical devices, such as flow batteries, fuel cells and electrolysers, is critical for the transition to a sustainable economy. Given the critical role of porous electrodes in the performance of these devices, understanding their structure-function relationship is crucial. Although porous electrodes with many different internal structures have been utilized, there is no clear consensus as to what features lead to what aspects of electrode performance. Transport in porous electrodes is commonly approximated by mean-field theories, which assumes a homogenous, Darcy-like permeability in the porous structure. Recent findings have challenged the suitability of these assumptions by revealing extreme heterogeneities in the electrolyte transport, on commercially relevant length scales exceeding the electrode pore size by an order of magnitude. [1] In this study, we introduce a new analytical method for electrochemical flow devices: 4D Confocal Optical Fluorescence Microscopy. This non-invasive in-situ analytical technique distinguishes between oxidized and reduced molecular species by their fluorescence spectra and maps out 3D molecular concentration fields with single-digit micron resolution (Figure 1). 3D movies, correlated with macroscopic chronoamperometry, add time as a fourth dimension. Thus, electrochemical conversion and species advection and diffusion can be monitored at heretofore unprecedented resolution, giving us new routes to understanding local phenomena in porous electrodes. We demonstrate this method by monitoring the reversible electrolytic reduction of 2,7 anthraquinone disulfonate (AQDS) to its corresponding hydroquinone, H2AQDS, in aqueous electrolyte in a transparent electrochemical cell. We monitor changes in the concentration field as a response to the variation of applied potential and current in real time. We correlate the fluorescence intensity of a particular band of wavelengths to the electrolyte state of charge. Furthermore, high sensitivity to non-linear optical effects enables us to capture the reversible formation of a dimer, specific to the AQDS/H2AQDS system, quantitatively in an operating battery. This new high-resolution 4D technique of characterizing operando electrochemical devices is expected to provide insight into the relationship between electrode microstructure and electrochemical performance features. Literature cited: [1] A.A. Wong, S.M. Rubinstein and M.J. Aziz, “Direct visualization of electrochemical reactions and heterogeneous transport within porous electrodes in operando by fluorescence microscopy” Cell Reports Phys. Sci. 2021, 100388; https://doi.org/10.1016/j.xcrp.2021.100388 Figure 1