Semi-Dirac and Weyl fermions in transition metal oxides

We show that a class of compounds with I4/mcm crystalline symmetry hosts three-dimensional semi-Dirac fermions. Unlike the known two-dimensional semi-Dirac points, the degeneracy of these three-dimensional semi Dirac points is not lifted by spin-orbit coupling due to the protection by a nonsymmorphic symmetry-mirror reflection in the a -b plane and a translation along the c axis. This crystalline symmetry is found in tetragonal perovskite oxides, realizable in thin films by epitaxial strain that results in a(0)a(0)c(-)-type octahedral rotation. Interestingly, with broken time-reversal symmetry, two pairs of Weyl points emerge from the semi-Dirac points within the Brillouin zone, and an additional lattice distortion leads to an enhanced intrinsic anomalous Hall effect. The ability to tune the Berry phase by epitaxial strain can be useful in novel oxide-based electronic devices.