Weyl nodal point-line Fermion in ferromagnetic Eu$_5$Bi$_3$

Abstract

Based on $ab$ $initio$ calculations and low-energy effective $k{\cdot}p$ model, we propose a type of Weyl nodal point-line fermion, composed of 0D Weyl points and 1D Weyl nodal line, in ferromagnetic material Eu$_5$Bi$_3$. In the absence of spin-orbital coupling (SOC), the spin-up bands host a pair of triply degenerate points together with a unique bird-cage like node structure. In the presence of SOC with (001) magnetization, each triplet point splits into a double Weyl point and a single Weyl point accompanied by two nodal rings, forming two sets of Weyl nodal point-line fermions near the Fermi level. The novel properties of Weyl nodal point-line fermion are explored by revealing the unusual Berry curvature field and demonstrating the pinned chiral surface states with exotic Fermi arcs at different planes. Moreover, a large anomalous Hall conductivity of -260 ($\hbar$/$e$)($\Omega$cm)$^{-1}$ parallel to [001] direction is predicted. Our work offers a new perspective for exploring novel topological semimetal states with diverse band-crossing dimensions, and provides an ideal material candidate for future experimental realiztion.