Superdiffusive transport protected by topology and symmetry in all dimensions

Abstract

Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far been proposed on fine-tuned, artificial Hamiltonians, posing a significant challenge for experimental observation. In this work, we propose a broad class of models for generating superdiffusion potentially realizable in condensed matter systems across different spatial dimensions. A robust nodal structure emerges from the hybridization between the itinerant electrons and the local impurity orbitals, protected by the intrinsic symmetry and topology of the electronic band. We derive a universal scaling law for the conductance, $G \sim L^{-\gamma}$, revealing how the exponent is dictated by the dimensionality of the nodal structure ($D_{\text{node}}$) and its order $n$, and the dimensionality of the system $(D)$ at high temperatures or that of the Fermi surface ($D^F$) at low temperatures. Through numerical simulations, we validate these scaling relations at zero temperature for various models, including those based on graphene and multi-Weyl semimetals, finding excellent agreement between our theory and the computed exponents. Beyond the scaling of conductance, our framework predicts a suite of experimentally verifiable signatures, notably a new mechanism for linear-in-temperature resistivity ($\rho \sim T$) and a divergent low-frequency optical conductivity ($\sigma(\omega) \sim \omega^{\gamma -1}$), establishing a practical route to discovering and engineering anomalous transport in quantum materials.