Berry phase mechanism for optical gyrotropy in stripe-ordered cuprates

Optical gyrotropy, the lifting of degeneracy between left and right\ncircularly polarized light, can be generated by either time-reversal or chiral\nsymmetry breaking. In the high-$T_c$ superconductor La$_{2-x}$Ba$_x$CuO$_4$\n(LBCO), gyrotropy onsets at the same temperature as charge stripe order,\nsuggesting that the rotation of the stripe direction from one plane to the next\ngenerates a helical pattern that breaks chiral symmetry. In order to further\ntest this chiral stacking hypothesis it is necessary to develop an\nunderstanding of the physical mechanism by which chirality generates gyrotropy.\nIn this paper we show that optical gyrotropy is a consequence of Berry\ncurvature in the momentum space of chiral metals. We describe a physical\npicture showing that gyrotropy in chiral metals is closely related to the\nanomalous Hall effect in itinerant ferromagnets. We then calculate the\nmagnitude of the gyrotropic response for a given Berry curvature using the\nsemiclassical picture of anomalous velocity and Boltzmann transport theory. To\nconnect this physical picture with experiment, we calculate the Berry curvature\nin two tight-binding models. The first model is motivated by the structure of\nLBCO and illustrates how the gyrotropy is created when the stripe perturbations\nare added to a simple cubic model. In the second model, we examine the dramatic\nenhancement of the gyrotropic coefficient when Rashba spin-orbit coupling is\nintroduced. The magnitude of the rotation of polarization on reflection\nexpected based these models is calculated and compared with experimental data.\n