Topological phases of matter have established a new paradigm in physics, bringing quantum phenomena to the macroscopic scale and hosting exotic emergent quasiparticles. In this thesis, I demonstrate with my collaborators the first Weyl semimetal, TaAs, using angle-resolved photoemission spectroscopy (ARPES), directly observing its emergent Weyl fermions and topological Fermi arc surface states (Science 349, 6248 (2015); Physical Review Letters 116, 066802 (2016)). Next, I consider structurally chiral crystals, which I argue are guaranteed to host exotic chiral fermions leading to giant topological Fermi arcs. I study the chiral crystals RhSi and CoSi and I discover high-degeneracy chiral fermions with wide topological energy window, maximal separation in momentum space and giant Fermi arcs (Nature 567, 500 (2019); Nature Materials 17, 978 (2018)). I establish a natural relationship between structural and topological chirality, producing a robust topological state which we predict supports a four-unit quantized photogalvanic effect (Physical Review Letters 119, 206401 (2017)).
Next, I discuss the first quantum topological superlattice (Science Advances 3, e1501692 (2017)). I study multilayer heterostructures of alternating topological and trivial insulators. The Dirac cones at each interface tunnel across layers, realizing a new kind of emergent superlattice, where the interfaces act as lattice sites and the Dirac cones act as atomic orbitals. Adjusting the stacking pattern offers unprecedented control of individual hopping parameters in the atomic chain. I realize a novel topological phase transition and I predict that this platform may allow particle-hole symmetry without superconductivity.
Lastly, I present the discovery of a room-temperature topological magnet (arXiv:1712.09992). I study crystals of Co2MnGa and I observe a topological invariant supported by the material’s intrinsic magnetic order (Physical Review Letters 119, 156401 (2017)). In particular I observe topological Weyl lines and drumhead surface states by ARPES and, through a scaling analysis of the anomalous Hall transport response, I find that the large anomalous Hall effect in Co2MnGa arises from the Weyl lines. I hope that my discovery of Co2MnGa establishes topological magnetism as a new research frontier in condensed matter physics.