A long-standing controversial issue in the quest to understand the superconductivity in cuprates is the nature of the enigmatic pseudogap region of the phase diagram 1 . Especially important is whether the pseudogap state is a distinct thermodynamic phase characterized by broken symmetries below the onset temperature T * . Here we report torque-magnetometry measurements of anisotropic susceptibility within the ab planes in orthorhombic YBa 2 Cu 3 O y with exceptionally high precision. The in-plane anisotropy displays a significant increase with a distinct kink at the pseudogap onset temperature T * , showing a remarkable scaling behaviour with respect to T/T * in a wide doping range. Our systematic analysis reveals that the rotational symmetry breaking sets in at T * in the limit where the e ect of orthorhombicity is eliminated. These results provide thermodynamic evidence that the pseudogap onset is associated with a second-order nematic phase transition, which di ers from the recently reported charge-density-wave transition that accompanies translational symmetry breaking [2][3][4][5][6][7][8][9][10] . The pseudogap state harbours anomalous electronic states such as Fermi arcs, charge density waves (CDW), and d-wave superconductivity 1 . Electronic nematicity, a four-fold (C 4 ) rotational symmetry breaking, has emerged as a key feature inside the pseudogap regime 11-14 , but the presence or absence of a nematic phase transition and its relationship to the pseudogap remain unresolved. Nematicity has been widely discussed in cuprates, and one of its mechanism is the onset of a stripe-type CDW order parameter which generally breaks rotation symmetry as well as translation symmetry with a nonzero wavenumber Q = 0 (refs 2-10,15-18). In Bi 2 Sr 2 CaCu 2 O 8+δ (BSCCO), scanning tunnelling microscopy experiments at low temperatures report an electronic state, consisting of short-range CDW of unidirectional (one-dimensional, 1D) type with a period of ∼4a 0 , where a 0 is the Cu-O-Cu distance 19,20 . This nano-stripe structure persists even well above the superconducting transition temperature T c (ref. 21). In YBa 2 Cu 3 O y (YBCO), the short-range CDW order forms a dome-shaped boundary inside the pseudogap regime 6,7 . Resonant X-ray scattering (RXS) experiments in YBCO report that the CDW is of unidirectional type with a periodicity of ∼3a 0 (ref. 4).In both BSCCO and YBCO, the CDW forms domains with a size of ∼3 nm in zero field, inside which the C 4 symmetry of the unit cell is strongly broken. In contrast to such CDW orders, the nematicity may also be caused by an instability without breaking translational symmetry, characterized by Q = 0.The measurement of the magnetic torque has a very high sensitivity for detecting magnetic anisotropy. The torque τ = µ 0 V M × H is a thermodynamic quantity, a differential of the free energy with respect to angular displacement. Here µ 0 is the permeability of vacuum, V is the sample volume, and M is the magnetization induced by the external magnetic field H. When H is rotated ...
In metals, orbital motions of conduction electrons on the Fermi surface are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators. Here, we report a notable exception in an insulator-ytterbium dodecaboride (YbB). The resistivity of YbB, which is of a much larger magnitude than the resistivity in metals, exhibits distinct quantum oscillations. These unconventional oscillations arise from the insulating bulk, even though the temperature dependence of the oscillation amplitude follows the conventional Fermi liquid theory of metals with a large effective mass. Quantum oscillations in the magnetic torque are also observed, albeit with a lighter effective mass.
We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the ab plane. At low temperatures, the upper critical field µ0H ab c2 shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at µ0H * ≈ 24 T well below µ0H ab c2 , indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the highfield phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe.Exotic superconductivity with a nontrivial Cooperpairing state has been a longstanding issue of interest in condensed-matter physics. Among possible exotic states, a spatially nonuniform superconducting state in the presence of strong magnetic fields caused by the paramagnetism of conduction electrons has been the subject of great interest after the pioneering work by Fulde and Ferrell as well as Larkin and Ovchinnikov (FFLO) [1,2]. In the FFLO state, pair breaking due to the Pauli paramagnetic effect is reduced by forming a new pairing state (k↑, −k + q↓) with |q| ∼ gµ B H/ υ F (υ F is the Fermi velocity, g the g-factor, and µ B the Bohr magneton) between Zeeman split parts of the Fermi surface, instead of (k↑, −k↓) pairing in BCS superconductors [Figs. 1(a) and 1(b)]. The fascinating aspect of the FFLO state is that the superconducting order parameter, in its simplest form, is modulated as ∆ ∝ sin q · r, and periodic planar nodes appear perpendicular to the magnetic field near the upper critical field H c2 , leading to a segmentation of the vortices into pieces of length Λ = π/|q| [ Fig. 1(c)].Despite tremendous efforts in the search for the FFLO states in the past half century, indications of its experimental realization have been reported in only a few candidate materials, including quasi-two-dimensional (2D) organic superconductors and the heavy-fermion superconductor CeCoIn 5 [3-5]. In both systems, a thermodynamic phase transition occurs below H c2 and a high-field superconducting phase emerges at low temperatures [6][7][8][9]. In the former, each superconducting layer is very weakly coupled via the Josephson effect. The FFLO state is observed in a magnetic field H applied parallel to the layers, where the magnetic flux is concentrated in the regions between the layers forming coreless Josephson vortices. Therefore, the segmentation of the vortices by FFLO nodes, which is one of the most fascinating properties of the FFLO state, is not expected. The presence of the FFLO...
The emergence of the nematic electronic state that breaks rotational symmetry is one of the most fascinating properties of the iron-based superconductors, and has relevance to cuprates as well. FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering, providing a significant opportunity to investigate the role of nematicity in the superconducting pairing interaction. Here, to reveal how the superconducting gap evolves with nematicity, we measure the thermal conductivity and specific heat of FeSe S , in which the nematicity is suppressed by isoelectronic sulfur substitution and a nematic critical point (NCP) appears at [Formula: see text] We find that, in the whole nematic regime ([Formula: see text]), the field dependence of two quantities consistently shows two-gap behavior; one gap is small but highly anisotropic with deep minima or line nodes, and the other is larger and more isotropic. In stark contrast, in the tetragonal regime ([Formula: see text]), the larger gap becomes strongly anisotropic, demonstrating an abrupt change in the superconducting gap structure at the NCP. Near the NCP, charge fluctuations of [Formula: see text] and [Formula: see text] orbitals are enhanced equally in the tetragonal side, whereas they develop differently in the orthorhombic side. Our observation therefore directly implies that the orbital-dependent nature of the nematic fluctuations has a strong impact on the superconducting gap structure and hence on the pairing interaction.
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