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On the basis of the microscopic quasi-classical Eilenberger theory, weanalyze the recent angle-resolved specific heat experiment carried out at lowtemperature for Sr$_2$RuO$_{4}$ to identify the superconducting gap symmetry,comprising either horizontal or vertical line nodes relative to the tetragonalcrystal symmetry. Several characteristics, in particular, the landscape of thein-plane oscillation amplitude $A_4(B, T)$ with a definite sign for almost theentire $B$-$T$ plane are best explained by the horizontal line node symmetry,especially when the multiband effect and Pauli paramagnetic effect are takeninto account. The present analysis of $A_4(B,T)$ with definite sign points tothe presence of an anomalous field region at a lower temperature in theexperimental data, whose origin is investigated. Our theory demonstrates theapplication and uniqueness of the field-rotating thermodynamic measurements inuncovering the precise gap structure for target materials.

Theoretical studies for identifying horizontal line nodes via angle-resolved density of states measurements ---Application to Sr$_2$RuO$_{4}$---