Theoretical studies for identifying horizontal line nodes via angle-resolved density-of-states measurements: Application to Sr2RuO4

On the basis of the microscopic quasiclassical Eilenberger theory, we analyze the recent angle-resolved specific heat experiment carried out at low temperature for ${\mathrm{Sr}}₂{\mathrm{RuO}}₄$ to identify the superconducting gap symmetry, comprising either horizontal or vertical line nodes relative to the tetragonal crystal symmetry. Several characteristics, in particular, the landscape of the in-plane oscillation amplitude ${A}₄(B,T)$ with a definite sign for almost the entire $B\text{\ensuremath{-}}T$ plane are best explained by the horizontal line node symmetry, especially when the multiband and Pauli paramagnetic effects are taken into account. The present analysis of ${A}₄(B,T)$ with definite sign points to the presence of an anomalous field region at a lower temperature in the experimental data, whose origin is investigated. Our theory demonstrates the application and uniqueness of the field-rotating thermodynamic measurements in uncovering the precise gap structure for target materials.