Abstract: Over the last decade, the concept of Dirac matter has emerged to the forefront of condensed matter physics. Prominent examples include the physics of the Dirac point in graphene, Weyl points in topological semi-metals (TaAs), and edge states in topological insulators (Bi2Te3). These phases of matter are a playground for studying effects related to the relativistic Dirac equation. We note that they are defined only with respect to the properties of the electron (e.g., bandstructure). Therefore, it is still an open question whether Maxwell’s equations, which are relativistically invariant similar to the Dirac equation, predict fundamentally new phases of matter. In this talk, we will conclusively answer this question.
We also introduce a theoretical framework to search for Maxwellian phases of matter by comparing the symmetries between the Dirac equation and Maxwell’s equations. These underlying symmetries are fundamentally tied to the spin-statistics theorem. In particular, the rigorous definition of photon energy density, spin, and mass inside matter is a long-standing question that is answered by our theory. Using our approach, we predict that there could exist many such intriguing phases in nature.
We show that the fundamental requirements for the existence of Maxwellian phases are nonlocality and dispersion in the conductivity tensor of matter (𝜎𝜎⃡(𝜔𝜔,𝑞𝑞)). Thus, the Berry gauge field is induced through the frequency and momentum dependence of optical response parameters and not through periodic structuring or periodic time modulation.