Superdiffusive transport protected by topology and symmetry in all dimensions
ORAL
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 potentially realizable models for generating superdiffusion 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 ~ L-γ, revealing how the exponent is dictated by the dimensionality of the nodal structure (Dnode) and its order n, and the dimensionality of the system D at high temperatures or that of the Fermi surface (DF) 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 (⍴ ~ T) and a divergent low-frequency optical conductivity.
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 potentially realizable models for generating superdiffusion 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 ~ L-γ, revealing how the exponent is dictated by the dimensionality of the nodal structure (Dnode) and its order n, and the dimensionality of the system D at high temperatures or that of the Fermi surface (DF) 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 (⍴ ~ T) and a divergent low-frequency optical conductivity.
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Presenters
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Shaofeng Huang
- Chinese Academy of Sciences,Institute of Physics