A numerical calculation of the electronic specific heat for the compound Sr$_2$RuO$_4$ below its superconducting transition temperature

Abstract

In this work, a numerical study of the superconducting specific heat of the unconventional multiband superconductor Strontium Ruthenate is performed. Two band gaps models are employed, and the results rendered for each of them are compared. One of the models, previously proposed by one of the authors to explain the experimental temperature behavior of the ultrasound attenuation, considers two gaps with point nodes of different magnitude on different gap surface sheets, while the other one is an isotropic and line node model, reported in the literature for describing quantitatively experimental specific heat data. The superconducting density of states DOS is computed by employing these two models and then, a detailed numerical study of the electronic specific heat, that includes the contribution from the different Fermi sheets, is carried out. It is found that the calculated point node model specific heat temperature behavior shows an excellent agreement with the existent Sr$_2$RuO$_4$ experimental data at zero field, particularly, it is obtained that the observed specific heat jump at T$_c$ is precisely reproduced. Also, it is found that the sum of the contributions from the different bands fits quantitatively the measured specific heat data. The results in this work evidence that the Sr$_2$RuO$_4$ superconducting states are of unconventional nature, corresponding to those of a point node superconductor, and show the importance of taking into account the multiband nature of the material when calculating thermodynamic superconducting quantities.