Non-linear Hall Effect in Two- and Three-dimensional Materials

Abstract

Underpinned by the concept of Berry curvature in band theory, the family of classical and quantized Hall effects are conventionally observed in the linear response regime. A measurable Hall response requires the time-reversal (TR) symmetry to be broken, either by an external magnetic field or internal magnetization. Recently, a new addition to the Hall effect family, a non-linear Hall (NLH) response, has been proposed in systems that preserve TR symmetry. The intrinsic contribution to this NLH current originates from Berry curvature dipole (BCD), the first-order moment of Berry curvature. BCD emerges in non-centrosymmetric materials due to the asymmetric distribution of Berry curvature in the momentum space. Following the initial prediction, various materials have been theoretically predicted and experimentally confirmed to exhibit NLH response as a result of intrinsic (BCD) as well as extrinsic (disorder/skew scattering) effects. The identification and study of materials that display BCD can provide a better understanding of its underlying quantum nature, while being potential platforms to observe and engineer NLH effects and its expected applications. In this thesis, using first-principles density functional computations and tight-binding model calculations, we put forward different classes of materials, both two- and three-dimensional, as potential candidates that display NLH effect induced by a non-zero BCD. Among three-dimensional materials, we first look at systems that belong to chiral space groups, i.e., have structural chirality, as they are natural candidates for the study of BCD owing to the lack of improper symmetries. We study the nature of BCD in the pair of enantiomers using a simple chiral tight-binding model and density functional computations of real chiral materials. We demonstrate that the two enantiomeric pairs exhibit an opposite sign of the BCD and the resulting NLH response. We then propose oxide heterostructures, designed by sandwiching a thin film of heavy element metallic perovskite between a ferroelectric perovskite insulator, as another class of material that displays NLH effect. We demonstrate how tuning the number and type of central metallic layer can tune the nature of BCD in these systems. Among two-dimensional materials, with focus on the 1T’ phase of monolayer transition metal dichalcogenides, we investigate two different strategies for the engineering of BCD. By constructing Janus monolayers and heterostructures to break symmetries, we show how BCD can be effectively induced and tuned in such systems. In summary, this thesis presents promising material platforms to generate and tune non-linear Hall effects.