Optical Gyrotropy from Axion Electrodynamics in Momentum Space

Several emergent phenomena and phases in solids arise from configurations of the electronic Berry phase in momentum space that are similar to gauge field configurations in real space such as magnetic monopoles. We show that the momentum-space analogue of the “axion electrodynamics” term $\mathbf{E}·\mathbf{B}$ plays a fundamental role in a unified theory of Berry-phase contributions to optical gyrotropy in time-reversal invariant materials and the chiral magnetic effect. The Berry-phase mechanism predicts that the rotatory power along the optic axes of a crystal must sum to zero, a constraint beyond that stipulated by point-group symmetry, but observed to high accuracy in classic experimental observations on alpha quartz. Furthermore, the Berry mechanism provides a microscopic basis for the surface conductance at the interface between gyrotropic and nongyrotropic media.

Figure 1

Momentum-space representation of the Berry curvature mechanism for nonvanishing transverse current in a metal with inversion-symmetry breaking. The ellipsoid depicts a typical Fermi surface with slices oriented perpendicular to the optical wave vector. The Berry curvature, electron velocity, and acceleration to first order in an optical wave vector are illustrated for two points related by time reversal.

Figure 2

Illustration of a slab of an acentric metal in which electrons are depleted underneath a gate electrode. In the presence of an electromagnetic wave, counterpropagating sheet currents appear at the interfaces between optically active and inactive media.