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Since the discovery of topological insulators a lot of research effort has been devoted to magnetic topological materials, in which non-trivial spin properties can be controlled by magnetic fields, culminating in a wealth of fundamental phenomena and possible applications. The main focus was on ferromagnetic materials that can host Weyl fermions and therefore spin textured Fermi arcs. The recent discovery of Fermi arcs and new magnetic bands splitting in antiferromagnet (AFM) NdBi has opened up new avenues for exploration. Here we show that these uncharted effects are not restricted to this specific compound, but rather emerge in CeBi, NdBi, and NdSb when they undergo paramagnetic to AFM transition. Our data show that the Fermi arcs in NdSb have 2-fold symmetry, leading to strong anisotropy that may enhance effects of spin textures on transport properties. Our findings thus demonstrate that the RBi and RSb series are materials that host magnetic Fermi arcs and may be a potential platform for modern spintronics., 19 pages, five figures, supplemental information

We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. According to the parity formula proposed by Fu, Berg, and Sato, odd-parity pairing leads to conventional first-order topological superconductivity when a normal metal has an odd number of Fermi surfaces. Here, we derive generalized parity formulae for the topological invariants characterizing higher-order topology of centrosymmetric superconductors. Based on the formulae, we systematically classify all possible band structures of ferromagnetic metals that can induce inversion-protected higher-order topological superconductivity. Among them, doped ferromagnetic nodal semimetals are identified as the most promising normal state platform for higher-order topological superconductivity. In two dimensions, we show that odd-parity pairing of doped Dirac semimetals induces a second-order topological superconductor. In three dimensions, odd-parity pairing of doped nodal line semimetals generates a nodal line topological superconductor with monopole charges. On the other hand, odd-parity pairing of doped monopole nodal line semimetals induces a three-dimensional third-order topological superconductor. Our theory shows that the combination of superconductivity and ferromagnetic nodal semimetals opens up a new avenue for future topological quantum computations using Majorana zero modes., 6+13 pages, 2+1 figures; accepted version

We study the homotopy classification of symmetry representations to describe the bulk topological invariants protected by the combined operation of a twofold rotation ${C}_{2z}$ and time-reversal $T$ symmetries. We define topological invariants as obstructions to having smooth Bloch wave functions compatible with a momentum-independent symmetry representation. When the Bloch wave functions are required to be smooth, the information on the band topology is contained in the symmetry representation. This implies that the $d$-dimensional homotopy class of the unitary matrix representation of the symmetry operator corresponds to the $d$-dimensional topological invariants. Here, we prove that the second Stiefel-Whitney number, a two-dimensional (2D) topological invariant protected by ${C}_{2z}T$, is the homotopy invariant that characterizes the second homotopy class of the matrix representation of ${C}_{2z}T$. As an application of our result, we show that the three-dimensional (3D) bulk topological invariant for the ${C}_{2z}T$-protected topological crystalline insulator proposed by C. Fang and L. Fu in Phys. Rev. B 91, 161105 (2015), which we call the 3D strong Stiefel-Whitney insulator, is identical to the quantized magnetoelectric polarizability. The bulk-boundary correspondence associated with the quantized magnetoelectric polarizability shows that the 3D strong Stiefel-Whitney insulator has chiral hinge states as well as 2D massless surface Dirac fermions. This shows that the 3D strong Stiefel-Whitney insulator has the characteristics of both the first- and the second-order topological insulators, simultaneously, which is in consistence with the recent classification of higher-order topological insulators protected by an order-two symmetry.