We treat the nonequilibrium motion of a single-impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\ensuremath{\sim}{t}^{d/(d+1)}$ for the $d$ -dimensional system with $d\ensuremath{\ge}2$. For nonzero temperature $T$ , this crosses over to diffusive motion at long times with diffusivity $D\ensuremath{\sim}{T}^{\ensuremath{-}(d\ensuremath{-}1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.We treat the nonequilibrium motion of a single-impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\ensuremath{\sim}{t}^{d/(d+1)}$ for the $d$-dimensional system with $d\ensuremath{\ge}2$. For nonzero temperature $T$, this crosses over to diffusive motion at long times with diffusivity $D\ensuremath{\sim}{T}^{\ensuremath{-}(d\ensuremath{-}1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.

arXiv:1201.1055Physical Review AApr 6, 20127 citations

Superdiffusive transport protected by topology and symmetry in all dimensions

Shaofeng Huang, Yu-Peng Wang, Jie Ren +1 more

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, $G \sim L^{-γ}$ , 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 ( $ρ\sim T$ ) and a divergent low-frequency optical conductivity ( $σ(ω) \sim ω^{γ-1}$ ), establishing a practical route to discovering and engineering anomalous transport in quantum materials.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, $G \sim L^{-γ}$, 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 ($ρ\sim T$) and a divergent low-frequency optical conductivity ($σ(ω) \sim ω^{γ-1}$), establishing a practical route to discovering and engineering anomalous transport in quantum materials.

cond-mat.mes-hallCross-listedarXiv:2511.09629Nov 14, 2025

d

-dimensional system with $d\ensuremath{\ge}2$. For nonzero temperature

T

, this crosses over to diffusive motion at long times with diffusivity $D\ensuremath{\sim}{T}^{\ensuremath{-}(d\ensuremath{-}1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.

G \sim L^{-γ}

, 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 (

ρ\sim T

) and a divergent low-frequency optical conductivity (

σ(ω) \sim ω^{γ-1}

), establishing a practical route to discovering and engineering anomalous transport in quantum materials.