2024/08/27 by Christopher Ard, Evan Camrud, Ard, Christopher +5 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Atomic and Subatomic Physics Research #Computational Physics and Python Applications #Condensed matter physics #FOS: Physical sciences #Hall effect #Magnetic Field Sensors Techniques #Magnetic field #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Physics #Quantum mechanics
paper · pdf · doi:10.48550/arxiv.2408.15195
openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
It is well recognized that interpreting transport experiment results can be challenging when the samples being measured are spatially nonuniform. However, quantitative understanding on the differences between measured and actual transport coefficients, especially the Hall effects, in inhomogeneous systems is lacking. In this work we use homogenization theory to find exact bounds of the measured or homogenized anomalous Hall conductivity (AHC) in inhomogeneous conductors under minimal assumptions. In particular, we prove that the homogenized AHC cannot exceed the bounds of the local AHC. However, in common experimental setups, anomalies that appear to violate the above bounds can occur, with a popular example being the "humps" or "dips" of the Hall hysteresis curves usually ascribed to the topological Hall effect (THE). We give two examples showing how such apparent anomalies could be caused by different types of inhomogeneities and discuss their relevance in experiments.