High-order quantum Hall effects driven by magnetic-field dipole: an analytical solution for two-dimension electron gases.

You-Ting Huang^1*, Ching-Hao Chang¹, Botsz Huang¹, Ali G. Moghaddam², Xiao Zhang³

¹物理學系, 國立成功大學, 臺南市, Taiwan
²Institute for Advanced Studies in Basic Sciences, Tampare University, Tampare, Finland
³(Leibniz Institute for Solid State and Materials Research, Dresden University of Technology, Dresden, Germany

* Presenter:You-Ting Huang, email:l26104115@gs.ncku.edu.tw

Nonlinear hall effects extending beyond the ordinary ones have long been a significant area of research with high application potential in condensed matter physics. The commonly discussed nonlinear Hall effect is induced by the Berry curvature dipole, known as “nonlinear anomalous Hall effect”. While scientists already have some basic understanding and simple models for this effect, it is limited to a few classes of materials with ultralow lattice symmetry. In this work, instead of the Berry curvature in momentum space, we use the actual magnetic field in real space to generate the nonlinear hall effect. We orient our magnetic-field dipole linearly along x-axis, spanning from negative to positive values. Using the operator formulism and our developed susceptibility formulae, we analytically calculate the quantum hall effects in higher order. Additionally, we employ the diagonalization approach method to numerically compute the case of a sinusoidal magnetic-field dipole, which is easier to create experimentally.

Keywords: nonlinear hall effect, magnetic-field dipole, opertaor formulism