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Recent intensive experimental studies revealed that (Y,Lu)Ni$_2$B$_2$C is ananisotropic s-wave superconductor. In addition, its gap function possesses deeppoint minima, whose ratio of the gap anisotropy is more than 10. On thetheoretical side, however, it is nontrivial to understand the origin of such apeculiar superconductivity. In the present paper, we propose a mechanism of thes-wave superconductivity with deep gap minima, based on the theoretical modelwhere strong electron-phonon coupling as well as the moderate magneticfluctuations coexist. By analyzing the strong coupling Eliashberg equation, wefind that s-wave superconducting gap function owing to the electron-phononcoupling becomes highly anisotropic as the magnetic fluctuations increases. Theset of model parameters for realizing the strong gap anisotropy in the presentmodel will be appropriate for (Y,Lu)Ni$_2$B$_2$C. According to the presentmechanism, (groups of) pair of gap minima appear at points on the Fermi surfacewhich are connected by the nesting vector ${\bf Q}$, in both cases of s-wavesuperconductors and non s-wave ones. We briefly discuss other superconductorswith highly anisotropic gap function, e.g., PrOs$_{4}$Sb$_{12}$ andNa$_{0.33}$CoO$_2$.Comment: 14 page

physical review. b, condensed matter and materials physics

Theory of anisotropic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>-wave superconductivity with point-node-like gap minima: Analysis of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">Y</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Lu</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ni</mml:mi></mml:…

Theory of anisotropics-wave superconductivity with point-node-like gap minima: Analysis of(Y,Lu)Ni