Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe1-xSx and FeSe1-xTex.

The quantum vortex liquid (QVL) is an intriguing state of type-II superconductors in which intense quantum fluctuations of the superconducting (SC) order parameter destroy the Abrikosov lattice even at very low temperatures. Such a state has only rarely been observed, however, and remains poorly understood. One of the key questions is the precise origin of such intense quantum fluctuations and the role of nearby non-SC phases or quantum critical points in amplifying these effects. Here we report a high-field magnetotransport study of FeSe1-xSx and FeSe1-xTex which show a broad QVL regime both within and beyond their respective electron nematic phases. A clear correlation is found between the extent of the QVL and the strength of the superconductivity. This comparative study enables us to identify the essential elements that promote the QVL regime in unconventional superconductors and to demonstrate that the QVL regime itself is most extended wherever superconductivity is weakest.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5.

The recently discovered kagome superconductors AV3Sb5 (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV3Sb5 is still lacking. Here we report the impurity effects in CsV3Sb5 using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV3Sb5 is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

Charge-neutral fermions and magnetic field-driven instability in insulating YbIr3Si7.

Kondo lattice materials, where localized magnetic moments couple to itinerant electrons, provide a very rich backdrop for strong electron correlations. They are known to realize many exotic phenomena, with a dramatic example being recent observations of quantum oscillations and metallic thermal conduction in insulators, implying the emergence of enigmatic charge-neutral fermions. Here, we show that thermal conductivity and specific heat measurements in insulating YbIr3Si7 reveal emergent neutral excitations, whose properties are sensitively changed by a field-driven transition between two antiferromagnetic phases. In the low-field phase, a significant violation of the Wiedemann-Franz law demonstrates that YbIr3Si7 is a charge insulator but a thermal metal. In the high-field phase, thermal conductivity exhibits a sharp drop below 300 mK, indicating a transition from a thermal metal into an insulator/semimetal driven by the magnetic transition. These results suggest that spin degrees of freedom directly couple to the neutral fermions, whose emergent Fermi surface undergoes a field-driven instability at low temperatures.

Discovery of mesoscopic nematicity wave in iron-based superconductors.

Nematicity is ubiquitous in the electronic phases of iron-based superconductors. The order parameter that characterizes the nematic phase has been investigated in momentum space, but its real-space arrangement remains largely unexplored. We use linear dichroism (LD) in a low-temperature laser­photoemission electron microscope to map out the nematic order parameter of nonmagentic FeSe and antiferromagnetic BaFe2(As0.87P0.13)2. In contrast to structural domains, which have atomic-scale domain walls, the LD patterns in both materials show peculiar sinusoidal waves of electronic nematicity with wavelengths more than 1000 times as long as the unit cell. Our findings put strong constraints on the theoretical investigation of electronic nematicity.

Pressure-induced reconstitution of Fermi surfaces and spin fluctuations in S-substituted FeSe.

FeSe is a unique high-[Formula: see text] iron-based superconductor in which nematicity, superconductivity, and magnetism are entangled with each other in the P-T phase diagram. We performed [Formula: see text]Se-nuclear magnetic resonance measurements under pressures of up to 3.9 GPa on 12% S-substituted FeSe, in which the complex overlap between the nematicity and magnetism are resolved. A pressure-induced Lifshitz transition was observed at 1.0 GPa as an anomaly of the density of states and as double superconducting (SC) domes accompanied by different types of antiferromagnetic (AF) fluctuations. The low-[Formula: see text] SC dome below 1 GPa is accompanied by strong AF fluctuations, whereas the high-[Formula: see text] SC dome develops above 1 GPa, where AF fluctuations are fairly weak. These results suggest the importance of the [Formula: see text] orbital and its intra-orbital coupling for the high-[Formula: see text] superconductivity.

Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidate α-RuCl3.

Half-integer thermal quantum Hall conductance has recently been reported for the two-dimensional honeycomb material α-RuCl3 We found that the half-integer thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The measured field-angular variation of the quantized thermal Hall conductance has the same sign structure as the topological Chern number of the pure Kitaev spin liquid. This observation suggests that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in α-RuCl3.

Strongly correlated superconductivity in a copper-based metal-organic framework with a perfect kagome lattice.

Metal-organic frameworks (MOFs), which are self-assemblies of metal ions and organic ligands, provide a tunable platform to search a new state of matter. A two-dimensional (2D) perfect kagome lattice, whose geometrical frustration is a key to realizing quantum spin liquids, has been formed in the π - d conjugated 2D MOF [Cu3(C6S6)] n (Cu-BHT). The recent discovery of its superconductivity with a critical temperature T c of 0.25 kelvin raises fundamental questions about the nature of electron pairing. Here, we show that Cu-BHT is a strongly correlated unconventional superconductor with extremely low superfluid density. A nonexponential temperature dependence of superfluid density is observed, indicating the possible presence of superconducting gap nodes. The magnitude of superfluid density is much smaller than those in conventional superconductors and follows the Uemura's relation of strongly correlated superconductors. These results imply that the unconventional superconductivity in Cu-BHT originates from electron correlations related to spin fluctuations of kagome lattice.

High-pressure phase diagrams of FeSe1-xTex: correlation between suppressed nematicity and enhanced superconductivity.

The interplay among magnetism, electronic nematicity, and superconductivity is the key issue in strongly correlated materials including iron-based, cuprate, and heavy-fermion superconductors. Magnetic fluctuations have been widely discussed as a pairing mechanism of unconventional superconductivity, but recent theory predicts that quantum fluctuations of nematic order may also promote high-temperature superconductivity. This has been studied in FeSe1-xSx superconductors exhibiting nonmagnetic nematic and pressure-induced antiferromagnetic orders, but its abrupt suppression of superconductivity at the nematic end point leaves the nematic-fluctuation driven superconductivity unconfirmed. Here we report on systematic studies of high-pressure phase diagrams up to 8 GPa in high-quality single crystals of FeSe1-xTex. When Te composition x(Te) becomes larger than 0.1, the high-pressure magnetic order disappears, whereas the pressure-induced superconducting dome near the nematic end point is continuously found up to x(Te) ≈ 0.5. In contrast to FeSe1-xSx, enhanced superconductivity in FeSe1-xTex does not correlate with magnetism but with the suppression of nematicity, highlighting the paramount role of nonmagnetic nematic fluctuations for high-temperature superconductivity in this system.

Quasiparticle Nodal Plane in the Fulde-Ferrell-Larkin-Ovchinnikov State of FeSe.

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper pairs condensed at finite momentum, has been a long-sought state that remains unresolved in many classes of fermionic systems, including superconductors and ultracold atoms. A fascinating aspect of the FFLO state is the emergence of periodic nodal planes in real space, but its observation is still lacking. Here we investigate the superconducting order parameter at high magnetic fields H applied perpendicular to the ab plane in a high-purity single crystal of FeSe. The heat capacity and magnetic torque provide thermodynamic evidence for a distinct superconducting phase at the low-temperature/high-field corner of the phase diagram. Despite the bulk superconductivity, spectroscopic-imaging scanning tunneling microscopy performed on the same crystal demonstrates that the order parameter vanishes at the surface upon entering the high-field phase. These results provide the first demonstration of a pinned planar node perpendicular to H, which is consistent with a putative FFLO state.

Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe.

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 µ_{0}H_{c2}^{ab} shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at µ_{0}H^{*}≈24 T well below µ_{0}H_{c2}^{ab}, 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 high-field 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.

Measuring magnetic field texture in correlated electron systems under extreme conditions.

Pressure is a clean, continuous, and systematic tuning parameter among the competing ground states in strongly correlated electron systems such as superconductivity and magnetism. However, owing to the restricted access to samples enclosed in high-pressure devices, compatible magnetic field sensors with sufficient sensitivity are rare. We used nitrogen vacancy centers in diamond as a spatially resolved vector field sensor for material research under pressure at cryogenic temperatures. Using a single crystal of BaFe2(As0.59P0.41)2 as a benchmark, we extracted the superconducting transition temperature, the local magnetic field profile in the Meissner state, and the critical fields. The method developed in this work offers a distinct tool for probing and understanding a range of quantum many-body systems.

Diagonal nematicity in the pseudogap phase of HgBa2CuO4+δ.

The pseudogap phenomenon in the cuprates is arguably the most mysterious puzzle in the field of high-temperature superconductivity. The tetragonal cuprate HgBa2CuO4+δ, with only one CuO2 layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the magnetic susceptibility anisotropy within the CuO2 plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy sets in below the pseudogap temperature T*, which provides thermodynamic evidence for a nematic phase transition with broken four-fold symmetry. Surprisingly, the nematic director orients along the diagonal direction of the CuO2 square lattice, in sharp contrast to the bond nematicity along the Cu-O-Cu direction. Another remarkable feature is that the enhancement of the diagonal nematicity with decreasing temperature is suppressed around the temperature at which short-range charge-density-wave formation occurs. Our result suggests a competing relationship between diagonal nematic and charge-density-wave order in HgBa2CuO4+δ.

Ultrafast nematic-orbital excitation in FeSe.

The electronic nematic phase is an unconventional state of matter that spontaneously breaks the rotational symmetry of electrons. In iron-pnictides/chalcogenides and cuprates, the nematic ordering and fluctuations have been suggested to have as-yet-unconfirmed roles in superconductivity. However, most studies have been conducted in thermal equilibrium, where the dynamical property and excitation can be masked by the coupling with the lattice. Here we use femtosecond optical pulse to perturb the electronic nematic order in FeSe. Through time-, energy-, momentum- and orbital-resolved photo-emission spectroscopy, we detect the ultrafast dynamics of electronic nematicity. In the strong-excitation regime, through the observation of Fermi surface anisotropy, we find a quick disappearance of the nematicity followed by a heavily-damped oscillation. This short-life nematicity oscillation is seemingly related to the imbalance of Fe 3dxz and dyz orbitals. These phenomena show critical behavior as a function of pump fluence. Our real-time observations reveal the nature of the electronic nematic excitation instantly decoupled from the underlying lattice.

Quantum Vortex Core and Missing Pseudogap in the Multiband BCS-BEC Crossover Superconductor FeSe.

FeSe is argued as a superconductor in the Bardeen-Cooper-Schrieffer Bose-Einstein condensation crossover regime where the superconducting gap size and the superconducting transition temperature T_{c} are comparable to the Fermi energy. In this regime, vortex bound states should be well quantized and the preformed pairs above T_{c} may yield a pseudogap in the quasiparticle-excitation spectrum. We performed spectroscopic-imaging scanning tunneling microscopy to search for these features. We found Friedel-like oscillations near the vortex, which manifest the quantized levels, whereas the pseudogap was not detected. These apparently conflicting observations may be related to the multiband nature of FeSe.

Electrical resistivity across a nematic quantum critical point.

Correlated electron systems are highly susceptible to various forms of electronic order. By tuning the transition temperature towards absolute zero, striking deviations from conventional metallic (Fermi-liquid) behaviour can be realized. Evidence for electronic nematicity, a correlated electronic state with broken rotational symmetry, has been reported in a host of metallic systems1-5 that exhibit this so-called quantum critical behaviour. In all cases, however, the nematicity is found to be intertwined with other forms of order, such as antiferromagnetism5-7 or charge-density-wave order8, that might themselves be responsible for the observed behaviour. The iron chalcogenide FeSe1-xSx is unique in this respect because its nematic order appears to exist in isolation9-11, although until now, the impact of nematicity on the electronic ground state has been obscured by superconductivity. Here we use high magnetic fields to destroy the superconducting state in FeSe1-xSx and follow the evolution of the electrical resistivity across the nematic quantum critical point. Classic signatures of quantum criticality are revealed: an enhancement in the coefficient of the T2 resistivity (due to electron-electron scattering) on approaching the critical point and, at the critical point itself, a strictly T-linear resistivity that extends over a decade in temperature T. In addition to revealing the phenomenon of nematic quantum criticality, the observation of T-linear resistivity at a nematic critical point also raises the question of whether strong nematic fluctuations play a part in the transport properties of other 'strange metals', in which T-linear resistivity is observed over an extended regime in their respective phase diagrams.

Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid.

The quantum Hall effect in two-dimensional electron gases involves the flow of topologically protected dissipationless charge currents along the edges of a sample. Integer or fractional electrical conductance is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. It has been predicted that quantum Hall phenomena can also be created by edge currents with a fundamentally different origin: the fractionalization of quantum spins. However, such quantization has not yet been observed. Here we report the observation of this type of quantization of the Hall effect in an insulating two-dimensional quantum magnet1, α-RuCl3, with a dominant Kitaev interaction (a bond-dependent Ising-type interaction) on a two-dimensional honeycomb lattice2-7. We find that the application of a magnetic field parallel to the sample destroys long-range magnetic order, leading to a field-induced quantum-spin-liquid ground state with substantial entanglement of local spins8-12. In the low-temperature regime of this state, the two-dimensional thermal Hall conductance reaches a quantum plateau as a function of the applied magnetic field and has a quantization value that is exactly half of the two-dimensional thermal Hall conductance of the integer quantum Hall effect. This half-integer quantization of the thermal Hall conductance in a bulk material is a signature of topologically protected chiral edge currents of charge-neutral Majorana fermions (particles that are their own antiparticles), which have half the degrees of freedom of conventional fermions13-16. These results demonstrate the fractionalization of spins into itinerant Majorana fermions and Z2 fluxes, which is predicted to occur in Kitaev quantum spin liquids1,3. Above a critical magnetic field, the quantization disappears and the thermal Hall conductance goes to zero rapidly, indicating a topological quantum phase transition between the states with and without chiral Majorana edge modes. Emergent Majorana fermions in a quantum magnet are expected to have a great impact on strongly correlated quantum matter, opening up the possibility of topological quantum computing at relatively high temperatures.

Unusual Thermal Hall Effect in a Kitaev Spin Liquid Candidate α-RuCl_{3}.

The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity κ_{xy} measurements in α-RuCl_{3}, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction J_{K}/k_{B}∼80 K, positive κ_{xy} develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at T_{N}=7 K, the sign, magnitude, and T dependence of κ_{xy}/T at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations.

Tuning the Pairing Interaction in a d-Wave Superconductor by Paramagnons Injected through Interfaces.

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials. A new approach to this most fundamental and hotly debated issue focuses on the role of interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures. Here we fabricate hybrid superlattices consisting of alternating atomic layers of the heavy-fermion superconductor CeCoIn_{5} and antiferromagnetic (AFM) metal CeRhIn_{5}, in which the AFM order can be suppressed by applying pressure. We find that the superconducting and AFM states coexist in spatially separated layers, but their mutual coupling via the interface significantly modifies the superconducting properties. An analysis of upper critical fields reveals that, upon suppressing the AFM order by applied pressure, the force binding superconducting electron pairs acquires an extreme strong-coupling nature. This demonstrates that superconducting pairing can be tuned nontrivially by magnetic fluctuations (paramagnons) injected through the interface.

Maximizing T c by tuning nematicity and magnetism in FeSe1-x S x superconductors.

A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature (T c). To address this issue, FeSe is a key material, as it exhibits a unique pressure phase diagram involving non-magnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe have considerable overlap, how each order affects superconductivity remains perplexing. Here we construct the three-dimensional electronic phase diagram, temperature (T) against pressure (P) and isovalent S-substitution (x), for FeSe1-x S x . By simultaneously tuning chemical and physical pressures, against which the chalcogen height shows a contrasting variation, we achieve a complete separation of nematic and antiferromagnetic phases. In between, an extended non-magnetic tetragonal phase emerges, where T c shows a striking enhancement. The completed phase diagram uncovers that high-T c superconductivity lies near both ends of the dome-shaped antiferromagnetic phase, whereas T c remains low near the nematic critical point.

Full-Gap Superconductivity Robust against Disorder in Heavy-Fermion CeCu_{2}Si_{2}.

A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have the opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu_{2}Si_{2} were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magnetic penetration depth λ(T) in CeCu_{2}Si_{2}. We find that the fully gapped state is robust against disorder, demonstrating that low-energy bound states, expected for sign-changing gap structures, are not induced by nonmagnetic impurities. This provides bulk evidence for s_{++}-wave superconductivity without sign reversal.