Hierarchy of the third-order anomalous Hall effect: from clean to disorder regime

• Main Authors: Barman, Chanchal K, Chattopadhyay, Arghya, Sarkar, Surajit, Zhu, Jian-Xin, Nandy, Snehasish
• Format: Journal Article
• Language: English
• Published: 12.09.2024
• Subjects: Physics - Materials Science; Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.2409.07993

The third-order anomalous Hall effect (TOAHE) driven by Berry connection polarizability in Dirac materials offers a promising avenue for exploring quantum geometric phenomena. We investigate the role of impurity scattering on TOAHE using the semiclassical Boltzmann framework, via a comparison of the intrinsic contributions (stemming from the Berry connection polarizability effect) with the extrinsic contributions caused by the disorder. To validate our theoretical findings, we employ a generalized two-dimensional low-energy Dirac model to analytically assess the intrinsic and extrinsic contributions to the TOAHE. Our analysis reveals distinct disorder-mediated effects, including skew scattering and side jump contributions. We also elucidate their intriguing dependencies on Fermi surface anisotropy and discuss opportunities for experimental exploration.