Electric field induced Berry curvature dipole and non-linear anomalous Hall effects in higher wave symmetric unconventional magnets

Abstract

We investigate the second-order anomalous Hall response in two-dimensional higher-wave symmetric magnets, including the recently discovered class of collinear magnets known as altermagnets, when subjected to a symmetry-breaking external electric field. In these systems, the first- and second-order anomalous Hall responses mediated by the first- and second-order multipoles of the Berry curvature over the occupied states vanish by symmetry. However, a symmetry-breaking dc electric field can induce a nonzero Berry curvature dipole by coupling to a non-vanishing quantum metric, also known as the Berry connection polarizability. An applied ac electric field can then generate a finite nonlinear transverse Hall effect characterized by a second harmonic response. In addition, the dc field itself can generate a finite third-order transverse Hall response. We discuss this remarkable effect in a class of higher-order symmetric unconventional magnets (of $p$, $d$, $f$, $g$, $i$