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--- en:projects [2018/10/09 05:58] – ariad
+++ en:projects [2018/10/21 10:32] – ariad
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  [{{ :research:plotg.png?200x120|The tight-binding result of c<sub>xy</sub> is compared with the prediction of the effective low-energy theory of the $p$-wave superconductor.}}]
-This work constitutes a significant breakthrough in our understanding of the anomalous charge response, c<sub>xy</sub> of //chiral superconductors//. It is established that in order to correctly apply the Streda formula for calculating c<sub>xy</sub> it is necessary to employ compact geometries that avoid edge effects. This, in turn, requires a careful analysis of the effect of //finite-radius// vortex nucleation that leads to a slight adjustment of the Streda formula. The modified Streda formula is then applied to calculate c<sub>xy</sub> for a //p<sub>x</sub> ± ip<sub>y</sub> // superconductor placed on a square lattice at zero magnetic field and zero vorticity. We show that $c_{xy}$ is a sum of two contributions, one which is non-universal and the other equals $\kappa/8\pi$, where $\kappa$ is the Chern number of the superconductor. Moreover, we note that c<sub>xy</sub> is proportional to the anomalous Hall conductivity, which in turn is proportional to the polar Kerr angle. Thus, these results should affect calculation of the polar Kerr effect, hence they are significant for the determination of the order parameter of superconductors.
+This work extend our understanding of the anomalous charge response, c<sub>xy</sub> of //chiral superconductors//. It is established that in order to correctly apply the Streda formula for calculating c<sub>xy</sub> it is necessary to employ compact geometries that avoid edge effects. This, in turn, requires a careful analysis of the effect of //finite-radius// vortex nucleation that leads to an adjustment of the Streda formula. The modified Streda formula is then applied to calculate c<sub>xy</sub> for a //p<sub>x</sub> ± ip<sub>y</sub> // superconductor placed on a square lattice at zero magnetic field and zero vorticity. We show that $c_{xy}$ is a sum of two contributions, one which is non-universal and the other equals $\kappa/8\pi$, where $\kappa$ is the Chern number of the superconductor. Moreover, we note that c<sub>xy</sub> is proportional to the anomalous Hall conductivity, which in turn is proportional to the polar Kerr angle. Thus, these results should affect the calculation of the polar Kerr effect, hence they are significant for the determination of the order parameter of superconductors.
 [[https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.104511|Daniel Ariad, Yshai Avishai and Eytan Grosfeld. "How vortex bound states affect the Hall conductivity of a chiral p±ip superconductor." Phy. Rev. B 98, 104511 (2018).]] [[https://arxiv.org/abs/1603.00840|arXiv:1603.00840.]] In addition, our study is summarized in {{:research:poster01.pdf|this poster}}.