Topological quantum properties of chiral crystals

In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y\(_{2}\)Ir\(_{2}\)O\(_{7}\)) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y\(_{2}\)Ir\(_{2}\)O\(_{7}\) and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter \(\theta=\pi\), may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.

Fermions in nature come in several types: Dirac, Majorana and Weyl are theoretically thought to form a complete list. Even though Majorana and Weyl fermions have for decades remained experimentally elusive, condensed matter has recently emerged as fertile ground for their discovery as low energy excitations of realistic materials. Here we show the existence of yet another particle - a new type of Weyl fermion - that emerges at the boundary between electron and hole pockets in a new type of Weyl semimetal phase of matter. This fermion was missed by Weyl in 1929 due to its breaking of the stringent Lorentz symmetry of high-energy physics. Lorentz invariance however is not present in condensed matter physics, and we predict that an established material, WTe\(_2\), is an example of this novel type of topological semimetal hosting the new particle as a low energy excitation around a type-2 Weyl node. This node, although still a protected crossing, has an open, finite-density of states Fermi surface, likely resulting in a plethora physical properties very different from those of standard point-like Fermi surface Weyl points.