Quasiparticle excitations in FeSe were studied by means of specific heat $\left(C\right)$ measurements on a high-quality single crystal under rotating magnetic fields. The field dependence of $C$ shows three-stage behavior with different slopes, indicating the existence of three gaps $({\mathrm{\Delta }}_1,{\mathrm{\Delta }}_2$, and ${\mathrm{\Delta }}_3)$. In the low-temperature and low-field region, the azimuthal angle $\left(\varphi \right)$ dependence of $C$ shows a fourfold symmetric oscillation with a sign change. On the other hand, the polar angle $\left(\theta \right)$ dependence manifests as an anisotropy-inverted twofold symmetry with unusual shoulder behavior. Combining the angle-resolved results and the theoretical calculation, the smaller gap ${\mathrm{\Delta }}_1$ is proved to have two vertical-line nodes or gap minima along the $k_z$ direction, and is determined to reside on the electron-type $\varepsilon$ band. ${\mathrm{\Delta }}_2$ is found to be related to the electron-type $\delta$ band, and is isotropic in the $ab$ plane but largely anisotropic out of the plane. ${\mathrm{\Delta }}_3$ residing on the hole-type $\alpha$ band shows a small out-of-plane anisotropy with a strong Pauli paramagnetic effect.

• Received 26 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.220505