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We analyze the behavior of the thermal conductivity in quasi-two- dimensional superconductors with line nodes. Motivated by measurements of the anisotropy between the interplane and intraplane thermal transport in CeIr In5 we show that a simple model of the open Fermi surface with vertical line nodes is insufficient to describe the data. We propose two possible extensions of the model taking into account (a) additional modulation of the gap along the axial direction of the open Fermi surface and (b) dependence of the interplane tunneling on the direction of the in-plane momentum. We discuss the temperature dependence of the thermal conductivity anisotropy and its low T limit in these two models and compare the results with a model with a horizontal line of nodes ("hybrid gap"). We discuss possible relevance of each model for the symmetry of the order parameter in CeIr In5, and suggest further experiments aimed at clarifying the shape of the superconducting gap. © 2007 The American Physical Society.

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Physical Review B - Condensed Matter and Materials Physics