Anomalous Hall Conductivity as an Intrinsic Property of a Tight-Binding Graph
Abstract
In a ballistic system, the anomalous dc Hall response generically depends on microscopic details, including the geometric embedding of the orbitals and the precise implementation of the measurement. Here, we consider the question under what circumstances the anomalous Hall conductivity can be regarded as an intrinsic property of a system. We show that the full dc Hall response σxyH becomes embedding-independent in the presence of relaxation by impurity scattering, although the individual (intrinsic) band and (extrinsic) side-jump and anomalous-distribution contributions to the Hall conductivity separately remain embedding-dependent. We further derive a symmetry criterion for when the band term itself becomes embedding-independent, but argue that this alone neither identifies it with the full Hall conductivity σxyH, nor makes it a reliable approximation for σxyH. More broadly, our results establish embedding dependence as a diagnostic of whether a response coefficient represents a stationary intrinsic property of a material or retains sensitivity to measurement protocol.
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BibTeX
@misc{andriyakhina2026anomalous,
title = {{Anomalous Hall Conductivity as an Intrinsic Property of a Tight-Binding Graph}},
author = {E. S. Andriyakhina and G. Lemut and P. W. Brouwer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37939},
eprint = {2610.37939},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37939},
}
RIS
TY - UNPB
TI - Anomalous Hall Conductivity as an Intrinsic Property of a Tight-Binding Graph
AU - E. S. Andriyakhina
AU - G. Lemut
AU - P. W. Brouwer
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37939
UR - https://arxiv.org/abs/2610.37939
AB - In a ballistic system, the anomalous dc Hall response generically depends on microscopic details, including the geometric embedding of the orbitals and the precise implementation of the measurement. Here, we consider the question under what circumstances the anomalous Hall conductivity can be regarded as an intrinsic property of a system. We show that the full dc Hall response σ_xy^H becomes embedding-independent in the presence of relaxation by impurity scattering, although the individual (intrinsic) band and (extrinsic) side-jump and anomalous-distribution contributions to the Hall conductivity separately remain embedding-dependent. We further derive a symmetry criterion for when the band term itself becomes embedding-independent, but argue that this alone neither identifies it with the full Hall conductivity σ_xy^H, nor makes it a reliable approximation for σ_xy^H. More broadly, our results establish embedding dependence as a diagnostic of whether a response coefficient represents a stationary intrinsic property of a material or retains sensitivity to measurement protocol.
ER -