Unconventional magnetoelectric conductivity and electrochemical response from dipole-like sources of Berry curvature

Abstract

We investigate the longitudinal magnetoelectric conductivity and nonlinear electrochemical response (ECR) of three-dimensional nodal-ring semimetals, including vortex nodal-rings (VNRs) and $\mathcal{P}\mathcal{T}$-symmetric nodal-rings (PTNRs), together with three-band Hopf semimetals (HSMs), using the semiclassical Boltzmann formalism. The nodal rings of the VNRs and PTNRs are taken to lie in the $k_z=0$ plane, whereas the nodal points of HSMs host isolated Berry-curvature (BC) dipoles whose axes are aligned along the $k_z$ direction. In VNRs, such dipoles may be viewed as forming a continuous distribution along the nodal ring, providing a useful connection between the two classes of systems. For collinear electric and magnetic ($\mathcal{B}$) fields applied along the anisotropy axis $\hat{\mathbf{z}}$, the linear response is computed exactly, displaying the presence of odd powers of $B_z$. For a two-node HSM with oppositely oriented BC-dipole axes, a competition between intranode and internode scattering plays out. We further analyse the nonlinear ECR, described by third-rank response tensors that relate the electrical current to the combined effects of an external electric field and a chemical-potential gradient. The surviving tensor components are shown to be completely determined by the tilt direction of the band structure. A comparison of the three systems reveals a close correspondence between the responses of VNRs and HSMs, while PTNRs display qualitatively different behavior. We attribute these similarities and differences to the topology of the BC field, namely dipole-like sources in VNRs and HSMs versus the ring-confined BC structure characteristic of PTNRs.

arXiv commentrevised substantially; 2-node results added