Optical Gyrotropy from Axion Electrodynamics in Momentum Space

Abstract

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 E • 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 α-quartz. Furthermore, the Berry mechanism provides a microscopic basis for the surface conductance at the interface between gyrotropic and nongyrotropic media.

Dichroism as a probe for parity-breaking phases of spin-orbit coupled metals

“…The same logic [18] also applies to d and g (g being the cross product of r and d). The same result has recently been pointed out in the Berry curvature approach by Zhong et al [16], since again, v and Ω B are orthogonal vectors (v being the cross product of E and Ω B ). The author has verified this using the FDMNES program (described below) for tellurium (Table 2), where the E1-M1 (electric dipole -magnetic dipole) interference terms are found to be traceless for the various edges studied (L 1 , L 2,3 , M 4,5 , N 4,5 ), noting that the E1-E2 (electric dipole -electric quadrupole) interference terms are traceless by definition.…”

“…Polar toroidal ordering has been seen in a number of multiferroics [12,13], and is also the basis for a novel theory of the pseudogap phase of cuprates by Varma and collaborators [14], following earlier theoretical suggestions of Gorbatsevich et al [15]. In general, there are several operator equivalents that can describe natural dichroism as listed in Table 1, including a recently advocated form involving the Berry curvature by Zhong, Orenstein and Moore [16].…”

Anatomy of the chiral magnetic effect in and out of equilibrium

“…The equilibrium CME is absent in this case, while the CME in free-streaming regime is − g 3 σ 0 B. Interestingly, the existence of CME in free streaming regime does not necessarily require the Berry curvature, but its value would be smaller by σ 0 B from the one with the Berry curvature. The importance of distinguishing the effects of the Berry curvature and of the magnetic moment has been also emphasized in the context of gyrotropic effect [34][35][36]. We emphasize again that the equilibrium CME in hydrodynamic regime, J = σ 0 B, is a consequence of the Berry curvature, independent of the physics of spin magnetic moment (g-factor).…”

Vector optical activity in the Weyl semimetal TaAs

“…These and related materials also show novel magnetoresistance phenomena, including evidence for the axial anomaly [9,10] predicted long ago by Nielsen and Ninomiya [11]. This axial anomaly can also cause circular dichroism and related chiral optical effects [1][2][3][4].…”

“…Implications this result has in regards to optical effects predicted for topological Weyl semimetals are discussed. Weyl semimetals are predicted to have a variety of novel optical effects due to their topological electronic structure [1][2][3][4]. But in the case of Weyl semimetals which exist because of inversion symmetry breaking, unusual optical effects can also arise depending on the space group of the lattice.…”