Tutorial 7: Nodal Semi-Metals in General (2D, Weyl, and Nodal Line Systems)

Topological semimetals are the newest addition to the topological field. They come in many varieties: Weyl, Dirac, Nodal lines, monopole lines, New Fermions, and many others. They exhibit topological protection of varying degrees to the opening of a gap in the spectrum, and exhibit novel phenomena such as negative magneto-resistence and non-linear transport upon the addition of electric and/or magnetic fields in the system. The topological semimetals also acquire interesting properties when gapped by superconductivity. The tutorial will review the mathematics describing these states of matter and explain their topological protection by introducing several topological indices that characterize the systems. The tutorial will also describe the plethora of phenomena existing in nodal semi-metallic systems with an emphasis on the chiral anomaly and non-local transport. The tutorial will then turn towards experiments. It will present and explain several main experiments in the field, such as chiral anomaly, negative magneto-resistance and surface state STM, as well as non-local transport under magnetic and electric fields.