Superdiffusive Transport Protected by Topology and Symmetry Reveals Universal Conductance Scaling in All Dimensions

Anomalous transport, specifically superdiffusion, represents a fascinating departure from conventional understandings of how particles move through materials, and Shaofeng Huang, Yu-Peng Wang, and Jie Ren, alongside colleagues at the Beijing National Laboratory for Condensed Matter Physics and the Institute of Physics, Chinese Academy of Sciences, have now identified a robust mechanism driving this behaviour. Existing theoretical explanations for superdiffusion often rely on complex, artificial systems, hindering real-world observation, but this research proposes a broad class of models demonstrating superdiffusion in potentially realisable condensed matter systems, regardless of their dimensionality. The team reveals that a stable nodal structure, arising from the interaction between electrons and localised impurities and protected by the material’s inherent symmetry, underpins this superdiffusion, and they derive a universal scaling law connecting the system’s dimensionality to the observed transport properties. Validating this theory through numerical simulations on materials like graphene and multi-Weyl semimetals, the researchers not only confirm their scaling predictions but also forecast experimentally detectable signatures, including a unique linear-in-temperature resistivity and a divergent low-frequency optical conductivity, paving the way for the discovery and engineering of materials exhibiting this unusual transport behaviour.

Topological Materials and Disordered Many-Body Systems

This extensive collection of research details investigations into condensed matter physics, focusing on topological materials, disordered systems, and the complex interactions within many-body systems. The work highlights materials exhibiting unusual electronic properties, particularly those arising from their topological characteristics and the influence of disorder, with a strong emphasis on understanding electron behavior, the impact of imperfections, and collective phenomena like superconductivity and magnetism. Computational techniques are frequently employed to model and understand these complex systems. Key themes include the study of topological insulators and semimetals, materials with unique surface states and robust electronic properties. Researchers utilize techniques like angle-resolved photoemission spectroscopy to probe the electronic band structure and symmetry-based indicators to identify new topological phases. Investigations into disordered systems explore how imperfections affect electron localization and conductivity, while many-body physics research focuses on understanding the collective behavior of electrons and the emergence of novel phases of matter.

Hybridization Drives Universal Superdiffusive Conductance Scaling

Scientists have uncovered a new mechanism for achieving superdiffusion, an unusual type of transport where particles spread faster than in normal diffusion. This breakthrough focuses on the hybridization, or mixing, of itinerant electrons with localized impurity orbitals, creating a unique electronic environment and a broad class of models potentially realizable in various materials and spatial dimensions. A robust nodal structure emerges from this hybridization, protected by the inherent symmetry and topology of the electronic band, leading to the observed superdiffusive transport. The team derived a universal scaling law for conductance, demonstrating how the exponent governing the rate of transport is dictated by the dimensionality of the nodal structure and the system’s dimensionality at different temperatures.

Specifically, the exponent at high temperature is determined by the interplay between the system’s dimensions and the nodal structure, while at low temperature, it is governed by the dimensions of the Fermi surface and the nodal manifold. Extensive numerical simulations validated these scaling relations across diverse models, including graphene and three-dimensional topological multi-Weyl semimetals, confirming the theoretical predictions and demonstrating the robustness of the nodal structure. Furthermore, the research predicts a crossover from superdiffusion to diffusion at a characteristic length scale, governed by the rate of non-nodal scattering. Beyond conductance scaling, the framework predicts several experimentally verifiable signatures.

The team anticipates a linear-in-temperature resistivity, arising from the interplay between nodal structures and residual electron-electron interactions, and a divergent low-frequency optical conductivity, indicative of enhanced transport from long-lived quasiparticles. Additionally, angle-resolved photoemission spectroscopy measurements should reveal a quasiparticle broadening scaling with momentum deviation from the node, providing a spectroscopic method to characterize the nodal structure. These predictions offer concrete pathways for identifying and engineering anomalous transport in materials.

Nodal Structures Enable Robust Superdiffusion

This work establishes a new mechanism for achieving superdiffusion, a type of anomalous transport, through the creation of robust “nodal structures” within materials. Researchers demonstrate that by hybridizing itinerant electrons with localized impurity orbitals, these nodal structures emerge, protected by the intrinsic symmetry of the electronic band. This approach offers a pathway to realizing superdiffusion in condensed matter systems across various spatial dimensions, moving beyond previous models that relied on finely tuned, artificial Hamiltonians. The team derived a universal scaling law governing conductance, revealing that the exponent is determined by the dimensionality of the nodal structure and the system’s dimensionality at different temperatures.

Validating this theory through numerical simulations on models based on graphene and multi-Weyl semimetals, they found excellent agreement between predicted and observed exponents. Beyond conductance scaling, the framework predicts experimentally verifiable signatures, including a linear-in-temperature resistivity and a divergent low-frequency optical conductivity, offering a practical route to discovering and engineering anomalous transport. Future research directions include exploring the impact of additional perturbations and investigating the potential for tailoring nodal structures to optimize transport characteristics in specific materials. This work provides a foundational understanding of anomalous transport and opens new avenues for designing materials with enhanced functionalities.