Gap structure of FeSe determined by angle-resolved specific heat measurements in applied rotating magnetic field

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 threestage behavior with different slopes, indicating the existence of three gaps (∆1, ∆2, and ∆3). In the low-temperature and low-field region, the azimuthal-angle (φ) dependence of C shows a fourfold symmetric oscillation with sign change. On the other hand, the polar-angle (θ) 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 ∆1 is proved to have two vertical-line nodes or gap minima along the kz direction, and is determined to reside on the electron-type ε band. ∆2 is found to be related to the electron-type δ band, and is isotropic in the ab-plane but largely anisotropic out of the plane. ∆3 residing on the hole-type α band shows a small out-of-plane anisotropy with a strong Pauli-paramagnetic effect.Superconducting (SC) gap structures are intimately related to the pairing mechanism, which is pivotal for high-temperature superconductors. This issue is crucial for FeSe because of the unexpectedly high superconducting temperature, T c , in this system. Although the initial T c is below 10 K [1], it can be easily enhanced to 37 K under pressure, [2,3] and to over 40 K by intercalating spacer layers [4]. Recently, a monolayer of FeSe grown on SrTiO 3 has even shown a sign of T c over 100 K [5,6]. FeSe manifests some intriguing properties, including a nematic state without long-range magnetic order [7], crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein-condensation (BEC) [8], and a Diraccone-like state [9][10][11], which are crucial to understanding high-T c superconductivity.Efforts have been made to elucidate FeSe's gap structure, and the presence of nodes [8,12] or deep minima [13][14][15][16] have been proposed. Even if the multi-gap structure is established [17,18], gap nodes or minima must still be located in the corresponding bands. Unfortunately, there have been few reports on this issue except for the recent Bogoliubov quasiparticle interference (BQPI) experiments, which found gap minima in both the α and ε bands [19]. However, there is still no bulk evidence of the locations of nodes or gap minima, and also no information about the gap from the δ band. More importantly, details of gap structure, including the three-dimensional (3D) locations of gap nodes or minima, remain unexplored. To solve these issues, a bulk technique capable of probing quasiparticle (QP) excitations with 3D angular resolution is needed. Field-angle-resolved specific heat (ARSH) measurement is an ideal tool for probing the density of states (DOS) of QPs without interference from surface effects; it is angle resolved because the lowlying QP excitations near the gap nodes (minima) are field-orientation dependent [20]. ARSH measurements have been well applied to investigating the locations and types of nod...

Vortex-core properties and vortex-lattice transformation in FeSe

“…On the other hand, for a superconductor with nodes in the gap, for example d-wave superconductors with line nodes, Volovik et al 62 pointed out that the Doppler shifts in the quasiparticle spectrum due supercurrents around a vortex core qualitatively modify the field dependence as γ(H) ∝ √ H. The field dependence of the specific heat coefficient is presented in Figure 4(b). The data deviate from both the linear (γ ∝ H) and square-root (γ ∝ √ H) behavior in agreement with other reports 63 . FeSe indeed is not a simple isotropic s-wave or nodal superconductor 12,57,64,65 .…”

On the Remarkable Superconductivity of FeSe and Its Close Cousins

“…Some more recent investigations on the specific heat tried to extract the order parameter on the different bands [124,[172][173][174][175] by fitting procedures. Measurements of field-angle dependent specific heat [176] found evidence for three distinct superconducting gaps, where the two smallest appear to be anisotropic and the smallest possibly nodal. The specific heat studies of references [124,[177][178][179] tend to assign nodal superconductivity to FeSe (Figure 9g), while reference [180] comes to the conclusion that the system is fully gapped.…”

Nematic pairing from orbital-selective spin fluctuations in FeSe

“…In this situation, the explanation of the observed anisotropy of the SC gaps in FeSe becomes intimately related to the understanding of the nematic transition itself. Extensive experimental studies on FeSe-based mate-rial, ranging from quasiparticle interference imaging 22,23 and ARPES measurements [24][25][26][27][28] , to thermal probes 29,30 , suggest that the SC gap in FeSe is highly anisotropic on both hole and electron pockets. By defining θ the angle formed with the k x axis measured with respect to the center of each pocket, one finds that the gap is larger at θ = 0 on the Γ pocket, where the predominant character in the nematic phase is xz 19,26,27 , and at θ = π/2 on the X pocket, where the dominant character is yz, Fig.…”