Shaofeng Huang | Searcharxiv

arXiv2026

Resolution of Topology and Geometry from Momentum-Resolved Spectroscopies

Extracting the complete quantum geometric and topological character of Bloch wavefunctions from experiments remains a challenge in condensed matter physics. Here, we resolve this by introducing the "wavefunction form factor" (WFF) matrix, a quantity directly constructible from intensities in momentum- and energy-resolved spectroscopies like ARPES and INS. We demonstrate that band topology is encoded in "spectral nodes" -- momentum-space points where the WFF determinant vanishes, providing a direct readout of topological invariants via a topological selection rule. Furthermore, when the number of independent probes exceeds the number of the target bands, our framework yields an effective band projector. This enables the determination of Wilson loop spectra and the extraction of an effective quantum geometric tensor, providing a model-independent measurement of the non-Abelian Berry curvature and quantum metric as resolved by the experimental probes.

cond-mat.mes-hall↗

arXiv2025

Superdiffusive transport protected by topology and symmetry in all dimensions

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.

cond-mat.mes-hall↗