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en:projects [2019/02/18 14:52]
ariad
en:projects [2019/02/18 15:15] (current)
ariad
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 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. 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}}.+[[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:posters:​poster01.pdf|this poster}}.
  
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 Realization of non-abelian quasi-particles known as Majorana fermions is an ongoing challenge for physicists exploring topological states of matter. Towards achieving this goal, we recently suggested that Josephson vortices in topological Josephson junctions (TJJ) would constitute such Majorana fermions and retain the exchange statistics of bulk vortices. We corroborated this hypothesis by finding the universal exchange phase of Josephson vortices. In order to do so, we derived the Hamiltonian governing the dynamics of a soliton in an annular Josephson junction. Our next step was to develop a procedure to calculate the Berry connection of systems that posses particle-hole symmetry. The procedure was applied to confirm that the Abelian phase due to the an exchange between a vortex in the bulk of a p-wave superconductor and a Josephson vortex is π/8. In addition, we suggested an experiment to measure it by. Realization of non-abelian quasi-particles known as Majorana fermions is an ongoing challenge for physicists exploring topological states of matter. Towards achieving this goal, we recently suggested that Josephson vortices in topological Josephson junctions (TJJ) would constitute such Majorana fermions and retain the exchange statistics of bulk vortices. We corroborated this hypothesis by finding the universal exchange phase of Josephson vortices. In order to do so, we derived the Hamiltonian governing the dynamics of a soliton in an annular Josephson junction. Our next step was to develop a procedure to calculate the Berry connection of systems that posses particle-hole symmetry. The procedure was applied to confirm that the Abelian phase due to the an exchange between a vortex in the bulk of a p-wave superconductor and a Josephson vortex is π/8. In addition, we suggested an experiment to measure it by.
  
-[[http://​link.aps.org/​doi/​10.1103/​PhysRevB.95.161401|Daniel Ariad and Eytan Grosfeld. "​Signatures of the topological spin of Josesphson vortices in topological superconductors."​ Phys. Rev. B 95, 161401(R) (2017)]] [[https://​arxiv.org/​abs/​1301.0538|arXiv:​1301.0538.]] In addition, our study is summarized in {{:​research:​soliton_poster.pdf|this poster}}.+[[http://​link.aps.org/​doi/​10.1103/​PhysRevB.95.161401|Daniel Ariad and Eytan Grosfeld. "​Signatures of the topological spin of Josesphson vortices in topological superconductors."​ Phys. Rev. B 95, 161401(R) (2017)]] [[https://​arxiv.org/​abs/​1301.0538|arXiv:​1301.0538.]] In addition, our study is summarized in {{:research:posters:​soliton_poster.pdf|this poster}}.
  
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 [[http://​onlinelibrary.wiley.com/​doi/​10.1002/​jgra.50170/​full|Ariad,​ D., and M. Gedalin. "The role pickup ions play in the termination shock."​ Journal of Geophysical Research: Space Physics 118.6 (2013): 2854-2862]]. [[https://​rdcu.be/​7Pyz|free-to-read full-text version.]] [[http://​onlinelibrary.wiley.com/​doi/​10.1002/​jgra.50170/​full|Ariad,​ D., and M. Gedalin. "The role pickup ions play in the termination shock."​ Journal of Geophysical Research: Space Physics 118.6 (2013): 2854-2862]]. [[https://​rdcu.be/​7Pyz|free-to-read full-text version.]]
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en/projects.txt · Last modified: 2019/02/18 15:15 by ariad

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