The gap structure of Sr 2 RuO 4 , which is a longstanding candidate for a chiral p-wave superconductor, has been investigated from the perspective of the dependence of its specific heat on magnetic field angles at temperatures as low as 0.06 K (∼ 0.04T c ). Except near H c2 , its fourfold specific-heat oscillation under an in-plane rotating magnetic field is unlikely to change its sign down to the lowest temperature of 0.06 K. This feature is qualitatively different from nodal quasiparticle excitations of a quasi-two-dimensional superconductor possessing vertical lines of gap minima. The overall specific-heat behavior of Sr 2 RuO 4 can be explained by Doppler-shifted quasiparticles around horizontal line nodes on the Fermi surface, whose in-plane Fermi velocity is highly anisotropic, along with the occurrence of the Pauli-paramagnetic effect. These findings, in particular, the presence of horizontal line nodes in the gap, call for a reconsideration of the order parameter of Sr 2 RuO 4 . Sr 2 RuO 4 , a layered-perovskite superconductor with T c =1.5 K, 1) has attracted enormous attention ever since Knight-shift experiments provided favorable evidence that it exhibits spin-triplet pairing. [2][3][4][5] Numerous experiments have demonstrated that Sr 2 RuO 4 has non s-wave properties, 6, 7) and some of the experimental reports indicate a degenerate order parameter. 8,9) The simple Fermi-surface topology of Sr 2 RuO 4 comprising of three cylindrical sheets (α, β, and γ) 10, 11) together with its well-characterized Fermi-liquid behavior has led to the construction of several theoretical models to describe superconductivity. 6) Among these models, a spin-triplet chiral p-wave pairing characterized by d = ∆ 0ẑ (k x ± ik y ) has been considered to be a promising candidate.However, several experimental facts exist that cannot be explained in the framework of this spin-triplet scenario. 12) A serious controversy is the mechanism of the first-order superconducting transition along with the H c2 limit induced by the in-plane magnetic field. [13][14][15][16] It is reminiscent of the Pauliparamagnetic effect that is not allowed in the spin-triplet scenario. The superconducting gap structure of Sr 2 RuO 4 is also a contentious issue. In general, a chiral p-wave gap opening on the cylindrical Fermi-surface sheets has no symmetryprotected node. Nevertheless, the gap amplitude of Sr 2 RuO 4 has been widely accepted to be modulated, and lines of deep minima (or nodes) are suggested to be present somewhere in the gap because of the power-law temperature dependence of various physical quantities. [17][18][19][20] Furthermore, universal heat transport has raised the possibility of a nodal gap. 18) Various gap structures including vertical and horizontal line node gaps have been proposed so far; [21][22][23][24][25] however, the location of gap minima has not yet been established.During this decade, field-angle-dependent measurements that probe quasiparticle density of states, N(E), have been developed as powerful tools for determining ...

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...

We investigate the band structure, nematic state and superconducting gap structure of two selected FeSe single crystals containing different amount of disorder. Transport and angle-resolved photoemission spectroscopy measurements show that the small amount of disorder has little effect to the band structure and the nematic state of FeSe. However, temperature and magnetic field dependencies of specific heat for the two samples are quite different. Wave-vector-dependent gap structure are obtained from the three dimensional field-angle-resolved specific heat measurements. A small gap with two vertical-line nodes or gap minima along the kz direction is found only in the sample with higher quality. Such symmetry-unprotected nodes or gap minima are found to be smeared out by small amount of disorder, and the gap becomes isotropic in the sample of lower quality. Our study reveals that the reported controversy on the gap structure of FeSe is due to the disorder-sensitive node-like small gap.

On the basis of the microscopic quasi-classical Eilenberger theory, we analyze the recent angle-resolved specific heat experiment carried out at low temperature for Sr 2 RuO 4 to identify the superconducting gap symmetry, comprising either horizontal or vertical line nodes relative to the tetragonal crystal symmetry. Several characteristics, in particular, the landscape of the in-plane oscillation amplitude A 4 (B, T) with a definite sign for almost the entire B-T plane are best explained by the horizontal line node symmetry, especially when the multiband effect and Pauli paramagnetic effect are taken into account. The present analysis of A 4 (B, T) with definite sign points to the presence of an anomalous field region at a lower temperature in the experimental data, whose origin is investigated. Our theory demonstrates the application and uniqueness of the field-rotating thermodynamic measurements in uncovering the precise gap structure for target materials.