Non-linear Hall effect in multi-Weyl semimetals

Abstract

In the presence of time reversal symmetry, a non-linear Hall effect can occur in systems without an inversion symmetry. One of the prominent candidates for detection of such Hall signals are Weyl semimetals. In this article, we investigate the Berry curvature induced second and third order Hall effect in multi-Weyl semimetals with topological charges n = 1, 2, 3. We use low energy effective models to obtain general analytical expressions and discover the presence of a large Berry curvature dipole in multi-Weyl semimetals, compared to usual (n = 1) Weyl semimetals. We also study the Berry curvature dipole in a realistic tight-binding lattice model and observe two different kinds of variation with increasing topological charge – these can be attributed to different underlying Berry curvature components. We provide estimates of the signatures of second harmonic of Hall signal in multi-Weyl semimetals, which can be detected experimentally. Furthermore, we predict the existence of a third order Hall signal in multi-Weyl semimetals. We derive the analytical expressions of Berry connection polarizability tensor, which is responsible for third order effects, using a low energy model and estimate the measurable conductivity. Our work can help guide experimental discovery of Berry curvature multipole physics in multi-Weyl semimetals.

Nonlinear Hall effects in two-dimensional moiré superlattices

“…对于二维材料, 要想有非零贝 里曲率偶极矩, 材料至多只能存在一条镜面对称 轴. 根据材料的对称性和贝里曲率, 理论计算指出, 在 三 维 外 尔 半 金 属 [11,[47][48][49][50][51] 、 三 维 拓 扑 绝 缘 体 [52] 、 二维过渡金属硫族化合物 [10,[53][54][55] 、二维莫尔超晶 格 [22,25,[27][28][29]31,32] 以及某些低对称性晶体 [56][57][58][59][60][61][62] 中可 以实现非线性霍尔效应.…”

Nonlinear Hall effect in Rashba systems with hexagonal warping

“…Following this discovery, nonlinear Hall signals have also been reported in materials such as Dirac semimetals [21], Kondo materials [22], WSe 2 [23,24], topological insulator surfaces [25], and oxide interfaces of LaAlO 3 /SrTiO 3 [26,27], among others. Very recently, third-order Hall signals have been theoretically predicted in multi-weyl semimetals [28], and detected experimentally in MoTe 2 [29].…”

Quantum nonlinear ac transport theory at low frequency

“…Nonlinear Hall effect [1][2][3][4] is the emerging frontier of condensed matter research [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Prominent nonlinear Hall phenomena include the second order Hall effect discovered in WTe 2 [19][20][21] as well as TaIrTe 4 [22], and the third order Hall effect verified in T d -MoTe 2 [23], etc.…”