A Primer on Weyl Semimetals: Down the Discovery of Topological Phases

Abstract: Recently discovered Weyl semimetals (WSM) have found special place in topological condensed matter studies for they represent first example of massless Weyl fermions found in condensed matter systems. A WSM shows gapless bulk energy spectra with Dirac-like point degeneracies, famously called Weyl nodes, which carry with themselves well defined chiralities and topologically protected chiral charges. One finds the Berry curvature of the Bloch bands to become singular, like in a magnetic monopole, at these Weyl nodes. Moreover, these systems feature topological surface states in the form of open Fermi arcs. In this review, we undergo a concise journey from graphene based Dirac physics to Weyl semimetals: the underlying Hamiltonians, their basic features and their unique response to external electric and magnetic fields in order to provide a basic walk-through of how the Weyl physics unfolded with time starting from the discovery of Graphene.