Connecting continuous models of quantum systems to complex networks: Application to electron transport in real-world one dimensional van der Waals materials

One-dimensional (1D) van der Waals (vdW) materials are feasible implementations to research 1D physics, enhance electron devices and develop novel ones. We study electron transport in complex networks representing 1D vdW systems. We map the 1D system into a network in which any quantum state is represented as a node, and each electron transition is encoded by a link. Link formation depends on whether the electron loses its phase, that is, on the transport class. For coherent transport, the Hamiltonian of a 1D chain is equivalent to the network Laplacian matrix and electron dynamics is modeled with continuous time quantum walks. For incoherent transport, the electron–phonon interaction cause electron phase loss and electron hooping, links appearing at Miller-Abraham hopping rates. Electron dynamics is modeled thus with continuous time random walks. We have obtained two main results. The first is that, for coherent transport, electron delocalization persists in the long term. The second one, for incoherent transport in a system with disorder, is that the quick growth of conductivity in a temperature range found is due to the network evolving to the small world feature, which improves the navigability of the network.