Gap structure of FeSe determined by field-angle-resolved specific heat measurements

Abstract

Quasiparticle excitations in FeSe were studied by means of specific heat ($C$) 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 ($\Delta_1$, $\Delta_2$, and $\Delta_3$). In the low-temperature and low-field region, the azimuthal-angle ($\phi$) dependence of $C$ shows a four-fold symmetric oscillation with sign change. On the other hand, the polar-angle ($\theta$) dependence manifests as an anisotropy-inverted two-fold symmetry with unusual shoulder behavior. Combining the angle-resolved results and the theoretical calculation, the smaller gap $\Delta_1$ 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. $\Delta_2$ 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. $\Delta_3$ residing on the hole-type $\alpha$ band shows a small out-of-plane anisotropy with a strong Pauli-paramagnetic effect.