Berry connection polarizability tensor and third-order Hall effect

Abstract

One big achievement in modern condensed matter physics is the recognition of the importance of various band geometric quantities in physical effects. As prominent examples, Berry curvature and the Berry curvature dipole are connected to the linear and the second-order Hall effects, respectively. Here, we show that the Berry connection polarizability (BCP) tensor, as another intrinsic band geometric quantity, plays a key role in the third-order Hall effect. Based on the extended semiclassical formalism, we develop a theory for the third-order charge transport and derive explicit formulas for the third-order conductivity. Our theory is applied to the two-dimensional (2D) Dirac model to investigate the essential features of the BCP and the third-order Hall response. We further demonstrate the combination of our theory with the first-principles calculations to study a concrete material system, the monolayer FeSe. Our work establishes a foundation for the study of third-order transport effects, and reveals the third-order Hall effect as a tool for characterizing a large class of materials and for probing the BCP in band structure.

7 pages, 4 figures

References in corpus (9)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• The electronic properties of graphene
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Superconductivity in single-layer films of FeSe with a transition temperature above 100 K
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• The key ingredients of the electronic structure of FeSe
• Monolayer FeSe on SrTiO${}_3$
• Gyrotropic Hall effect in Berry-curved materials
• Superconducting FeSe monolayer with milli-electron volt Fermi energy

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