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Efforts to understand the microscopic origin of superconductivity in the cuprates are dependent on knowledge of the normal state. The Hall number in the low-temperature, high-field limit n H (0) has a particular importance because, within conventional transport theory, it is simply related to the number of charge carriers, so its evolution with doping gives crucial information about the nature of the charge transport. Here we report a study of the high-field Hall coefficient of the single-layer cuprates Tl 2 Ba 2 CuO 6+δ (Tl2201) and (Pb/La)-doped Bi 2 Sr 2 CuO 6+δ (Bi2201), which shows how n H (0) evolves in the overdoped-so-called strange metal-regime of cuprates. We find that n H (0) increases smoothly from p to 1 + p, where p is the number of holes doped into the parent insulating state, over a wide range of doping. The evolution of n H correlates with the emergence of the anomalous linear-in-temperature term in the low-temperature in-plane resistivity. The results could suggest that quasiparticle decoherence extends to dopings well beyond the pseudogap regime.

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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 iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In this review, we critically examine these claims and highlight significant differences in the bulk physical properties of both systems. While there is now a large body of evidence supporting the presence of a (magnetic) QCP in the iron pnictides, the situation in the cuprates is much less apparent, at least for the end point of the pseudogap phase. We argue that the opening of the normal state pseudogap in cuprates, so often tied to a putative QCP, arises from a momentum-dependent breakdown of quasiparticle coherence that sets in at much higher doping levels but which is driven by the proximity to the Mott insulating state at half filling. Finally, we present a new scenario for the cuprates in which this loss of quasiparticle integrity and its evolution with momentum, temperature and doping plays a key role in shaping the resultant phase diagram.