Topological Electromagnetic Phases of Matter

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 Dirac equation and geometry of the electron wavefunction. We note, however, that they are defined only with respect to the properties of the electron (eg: bandstructure). Therefore, it is still an open question whether Maxwell’s equations and geometry of the photon wavefunction predict fundamentally new phases of matter. In this talk, we will conclusively answer this question.

Maxwell Matter: We introduce a theoretical framework to search for Maxwellian phases of matter by contrasting the symmetries between the Dirac equation and Maxwell’s equations. These underlying symmetries are fundamentally tied to the spinstatistics theorem. In particular, the rigorous definition of photon energy density, photon spin and photon mass inside matter is a long-standing question which is answered by our theory. Using our approach, we predict that there could exist multiple such intriguing phases in nature.

Fundamental Requirement: Non-local Hall Conductivity We show that the fundamental requirement for the existence of Maxwellian phases is non-locality and dispersion in the conductivity tensor of matter. Thus the Berry gauge field is induced through a fundamentally new mechanism: the global frequency and momentum dependence of optical response parameters.

Defining Characteristics of Maxwellian Phases of Matter:

1) They possess Maxwell points, the spin-1 bosonic counterparts of Weyl points, which can exist in the energy-momentum relationship of electromagnetic waves inside matter.
2) The non-local dynamical Hall coefficient behaves like a dynamical photon mass.
3) Spin-1 edge states of linearly dispersing photons at the boundary of the Maxwellian phase of matter with completely vanishing photon wavefunction. We emphasize that such a Maxwellian spin wave does not exist in any phase of matter known till date.
Finally, we will discuss approaches to experimentally detect such effects in condensed matter.

[1] Quantum Gyro-Electric Effect, T. Van Mechelen and Z. Jacob, Phys.Rev.A 98, 023842 (2018) [2] Photonic Dirac Monopoles and Skyrmions , T. Van Mechelen and Z. Jacob, Opt. Mat. Exp. (2018) [3] Unidirectional Maxwellian Spin Waves, T. Van Mechelen, Z. Jacob, Nanophotonics 8 (8) 1399 (2019) Fig 1: Searching for Maxwellian Phases of Matter [4] Nonlocal topological electromagnetic phases of matter, T. Van Mechelen and Z. Jacob, Phys. Rev. B 99 (20) 205 146 (2019)