Tunable Ergodicity of Adsorbates on Graphene with Substrate Potential Energy Landscape Engineering*

The motion of surface adsorbates over substrates remains of fundamental importance in condensed matter physics with applications in nanoscale molecular devices. Moire heterostructures, consisting of twisted layers of periodic two-dimensional materials, provide a promising route for modifying the substrate and device tunability through moire twist angle engineering. As of yet, the effects of moire substrate engineering on the diffusion of surface adsorbates has not been studied. Here, we model the diffusion of surface adsorbates on a graphene-BN moire heterostructure of varying periodicities using a continuous time Markov chain. We find that the potential energy landscape of the moire lattice induces a weak ergodicity breaking, changing the stochastic motion of adsorbates from Brownian motion to continuous time random walk.  Using a deep neural network, we demonstrate the ability to detect this transition using only a few hundreds of short single molecule tracks, which makes the analysis applicable under experimental constraints. This study illustrates a new mode for controlling the stochastic motion of molecules in nanoscale devices.