Topological Magnus responses in two- and three-dimensional systems

Abstract

Recently, time-reversal symmetric but inversion broken systems with nontrivial Berry curvature in the presence of a built-in electric field have been proposed to exhibit a new type of linear Hall effect in ballistic regime, namely, the Magnus Hall effect. The transverse current here is caused by the Magnus velocity that is proportional to the built-in electric field enabling us to examine the Magnus responses, in particular, Magnus Hall conductivity and Magnus Nernst conductivity, with chemical potential. Starting with two-dimensional (2D) topological systems, we find that warping induced asymmetry in both the Fermi surface and Berry curvature can in general enhance the Magnus response for monolayer graphene and surface states of topological insulator. The strain alone is only responsible for Magnus valley responses in monolayer graphene, while warping leads to finite Magnus response there. Interestingly, on the other hand, strain can change the Fermi surface character substantially that further results in distinct behavior of Magnus transport coefficients as we observe in bilayer graphene. These responses there remain almost insensitive to warping unlike the case of monolayer graphene. Going beyond 2D systems, we also investigate the Magnus responses in three-dimensional multi-Weyl semimetals (mWSMs) to probe the effect of tilt and anisotropic nonlinear energy dispersion. Remarkably, Magnus responses can only survive for the WSMs with chiral tilt. In particular, our study indicates that the chiral (achiral) tilt engenders Magnus (Magnus valley) responses. Therefore, Magnus responses can be used as a tool to distinguish between the untilted and tilted WSMs in experiments. In addition, we find that the Magnus Hall responses get suppressed with increasing the nonlinearity associated with the band touching around the multi-Weyl node.