The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ∼15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ∼6 GPa the sudden enhancement of superconductivity (Tc≤38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates.

When interacting electrons are confined to low-dimensions, the electron-electron correlation effect is enhanced dramatically, which often drives the system into exhibiting behaviours that are otherwise highly improbable. Superconductivity with the strongest electron correlations is achieved in heavy-fermion compounds, which contain a dense lattice of localized magnetic moments interacting with a sea of conduction electrons to form a three-dimensional (3D) Kondo lattice 1 . It had remained an unanswered question whether superconductivity would persist upon effectively reducing the dimensionality of these materials from three to two. Here we report on the observation of superconductivity in such an ultimately strongly-correlated system of heavy electrons confined within a 2D square-lattice of Ce-atoms (2D Kondo lattice), which was realized by fabricating epitaxial superlattices 2,3 built of alternating layers of heavy-fermion CeCoIn 5 4 and conventional metal YbCoIn 5 . The field-temperature phase diagram of the superlattices exhibits highly unusual behaviours, including a striking enhancement of the upper critical field relative to the transition temperature. This implies that the force holding together the superconducting electron-pairs takes on an extremely strong coupled nature as a result of two-dimensionalisation. The layered heavy-fermion compound CeCoIn 5 has the highest superconducting transition temperature (T c =2.3 K) among rare-earth-based heavy-fermion materials 4 . Its electronic properties are characterized by anomalously large value of the linear contribution to the specific heat (Sommerfeld coefficient ~1 J/mol K 2 ) indicating heavy effective masses of the 4f electrons which contribute greatly to the Fermi surface. The tetragonal CeCoIn 5 crystal structure is built from alternating layers of CeIn 3 and CoIn 2 stacked along the [001] direction. This compound possesses several key features for understanding the unconventional superconductivity in strongly correlated systems [5][6][7] . The superconductivity with d x 2 -y 2 pairing symmetry 8-11 which occurs in the proximity of a magnetic instability is a manifestation of magnetic fluctuations mediated superconductivity [5][6][7]12 .A very strong coupling superconductivity, where electron-pairs are bound together by strong forces, is revealed by a large specific heat jump 4 at T c representing a steep drop of the entropy below T c , and a large superconducting energy gap  needed to break the electron-pair , all indicate that the electronic, magnetic and superconducting properties are essentially 3D rather than 2D. Therefore it is still unclear to which extent the 3D nature is essential for the superconductivity of CeCoIn 5 .Recently the state-of-the-art technique has been developed to reduce the dimensionality of the heavy electrons in a controllable fashion by the layer-by-layer epitaxial growth of Ce-based materials. Previously a series of antiferromagnetic superlattices CeIn 3 /LaIn 3 have been successfully grown 2 , but it remains open whethe...

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.

We report a highly unusual angular variation of the upper critical field (Hc2) in epitaxial superlattices CeCoIn5(n)/YbCoIn5(5), formed by alternating layers of n and a 5 unit-cell thick heavy-fermion superconductor CeCoIn5 with a strong Pauli effect and normal metal YbCoIn5, respectively. For the n = 3 superlattice, Hc2(θ) changes smoothly as a function of the field angle θ. However, close to the superconducting transition temperature, Hc2(θ) exhibits a cusp near the parallel field (θ = 0 • ). This cusp behavior disappears for n = 4 and 5 superlattices. This sudden disappearance suggests the relative dominance of the orbital depairing effect in the n = 3 superlattice, which may be due to the suppression of the Pauli effect in a system with local inversion symmetry breaking. Taking into account the temperature dependence of Hc2(θ) as well, our results suggest that some exotic superconducting states, including a helical superconducting state, might be realized at high magnetic fields.PACS numbers: 74.25. Op, 81.15.Hi In the absence of time reversal symmetry or space inversion symmetry, the Fermi surface (FS) can often be split into portions with different spin structures. To stabilize superconductivity under such conditions where spin degeneracy is lifted, unconventional pairing of quasiparticles is needed, leading to exotic superconducting states very different from the conventional BCS pairing state of (k ↑, -k ↓). Considering the situation of the broken time reversal symmetry alone, Fulde and Ferrell [1], and Larkin and Ovchinnikov [2] proposed the pairing state of (k ↑, -k+q ↓) on a Zeeman-split FS. This so-called FFLO pairing state leads to the modulation of the superconducting order parameter in real space with the modulation wavelength of the order of 1/|q|. On the other hand, in the lack of space inversion symmetry, a Rashba-type spin-orbit coupling splits the FS into branches with spins of opposite rotation sense [3]. When the magnetic field is applied to such a system, a pairing state with a finite center-of-mass momentum can also be realized, resulting in a helical superconducting state analogous to the FFLO phase.However, such exotic superconducting states have been poorly explored because of the lack of suitable materials. Recent advancement in heavy fermion thin film fabrication technology [4,5] has enabled the preparation of superlattices formed by alternate stacking of c-axis oriented CeCoIn 5 and YbCoIn 5 with atomic layer thicknesses. The large Fermi velocity mismatch across the interface between CeCoIn 5 and YbCoIn 5 significantly reduces the transmission probability of quasiparticles, thereby ensuring quasi-two-dimensional superconductivity confined within CeCoIn 5 layers [6,7]. This provides a unique opportunity to explore the physics discussed above. This is because bulk CeCoIn 5 with strong Pauli effect has been reported to host the FFLO phase at low temperatures and high magnetic field [8][9][10][11]. In the superlattice, the electronic structure becomes two-dimensional, which is expec...

By using a molecular beam epitaxy technique, we fabricate a new type of superconducting superlattices with controlled atomic layer thicknesses of alternating blocks between heavy fermion superconductor CeCoIn5, which exhibits a strong Pauli pair-breaking effect, and nonmagnetic metal YbCoIn5. The introduction of the thickness modulation of YbCoIn5 block layers breaks the inversion symmetry centered at the superconducting block of CeCoIn5. This configuration leads to dramatic changes in the temperature and angular dependence of the upper critical field, which can be understood by considering the effect of the Rashba spin-orbit interaction arising from the inversion symmetry breaking and the associated weakening of the Pauli pair-breaking effect. Since the degree of thickness modulation is a design feature of this type of superlattices, the Rashba interaction and the nature of pair-breaking are largely tunable in these modulated superlattices with strong spin-orbit coupling.PACS numbers: 71.27.+a, 74.70.Tx, 74.78.Fk, 81.15.Hi Among the existing condensed matter systems, the metallic state with the strongest electron correlation effects is achieved in heavy fermion materials with 4f or 5f electrons. In these systems, a very narrow conduction band is formed at low temperatures through the Kondo effect. In particular, in Ce(4f )-based compounds, strong electron correlations within the narrow band strikingly enhance the quasiparticle effective mass. As a result of notable many-body effects, a plethora of fascinating physical phenomena including unconventional superconductivity with non-s-wave pairing symmetry appears [1]. The unconventional pairing symmetry and the associated exotic superconducting properties have mystified researchers over the past quarter century.Recently, it has been suggested that the inversion symmetry breaking (ISB) together with strong spin-orbit interaction can dramatically affect the superconductivity, giving rise to a number of novel phenomena such as anomalous magneto-electric effects [2] and topological superconducting states [3][4][5]. It has also been pointed out that such phenomena are more pronounced in strongly correlated electron systems [6]. The inversion symmetry imposes important constraints on the pairing states: In the presence of inversion symmetry, Cooper pairs are classified into a spin-singlet or triplet state, whereas in the absence of inversion symmetry, an asymmetric potential gradient ∇V yields a spin-orbit interaction that breaks parity, and the admixture of spin singlet and triplet states is possible [7,8]. For instance, asymmetry of the potential in the direction perpendicular to the two-dimensional (2D) plane ∇V [001] induces Rashbathe Fermi wave number, and σ is the Pauli matrix. Rashba interaction splits the Fermi surface into two sheets with different spin structures: the energy splitting is given by α R , and the spin direction is tilted into the plane, rotating clockwise on one sheet and anticlockwise on the other. When the Rashba splitting exceeds the superc...

When quantum fluctuations destroy underlying long-range ordered states, novel quantum states emerge. Spin-liquid (SL) states of frustrated quantum antiferromagnets, in which highly correlated spins fluctuate down to very low temperatures, are prominent examples of such quantum states. SL states often exhibit exotic physical properties, but the precise nature of the elementary excitations behind such phenomena remains entirely elusive. Here, we use thermal Hall measurements that can capture the unexplored property of the elementary excitations in SL states, and report the observation of anomalous excitations that may unveil the unique features of the SL state. Our principal finding is a negative thermal Hall conductivity κ xy which the charge-neutral spin excitations in a gapless SL state of the 2D kagomé insulator volborthite Cu 3 V 2 O 7 (OH) 2 · 2H 2 O exhibit, in much the same way in which charged electrons show the conventional electric Hall effect. We find that κ xy is absent in the high-temperature paramagnetic state and develops upon entering the SL state in accordance with the growth of the short-range spin correlations, demonstrating that κ xy is a key signature of the elementary excitation formed in the SL state. These results suggest the emergence of nontrivial elementary excitations in the gapless SL state which feel the presence of fictitious magnetic flux, whose effective Lorentz force is found to be less than 1/100 of the force experienced by free electrons.spin liquid | frustrated magnetism | thermal transport S pin liquids (SLs) are novel states which can occur in a magnetic system when the underlying magnetic order gives way to quantum fluctuations (1). In such states the constituent spins are highly correlated but continue to fluctuate strongly down to temperatures much lower than the spin-interaction energy scale, J. Novel notions such as emergent gauge fields, topological order, and fractionalized excitations have been associated with collective phenomena in SLs. In particular, both experiments (2-5) and theories (6-11) suggest that SL states display many unusual properties. It has been reported, for instance, that low-energy spin excitations in organic insulators with a triangular lattice structure behave like mobile carriers in a paramagnetic metal with a Fermi surface (2, 3), in contrast with the charge degree of freedom which is gapped. A description in terms of an SL state with fractionalized spin excitations was incorporated to account for the excitation continuum signal detected in a kagomé antiferromagnet (4). A magnetization transport measurement has shown that a pyrochlore frustrated magnet exhibits the characteristics of a supercooled SL state (5). Exotic quasi-particles such as spinons (6-8), visons (9, 10), and photons (11) have been predicted theoretically. Despite these intensive activities, the precise characters of the elementary excitations in SL states remain, from an experimental point of view, to be pinned down.In conducting systems, it is the charge-transport properties...

Strongly enhanced quantum fluctuations often lead to a rich variety of quantum-disordered states. Developing approaches to enhance quantum fluctuations may open paths to realize even more fascinating quantum states. Here, we demonstrate that a coupling of localized spins with the zero-point motion of hydrogen atoms, that is, proton fluctuations in a hydrogen-bonded organic Mott insulator provides a different class of quantum spin liquids (QSLs). We find that divergent dielectric behavior associated with the approach to hydrogen-bond order is suppressed by the quantum proton fluctuations, resulting in a quantum paraelectric (QPE) state. Furthermore, our thermal-transport measurements reveal that a QSL state with gapless spin excitations rapidly emerges upon entering the QPE state. These findings indicate that the quantum proton fluctuations give rise to a QSL—a quantum-disordered state of magnetic and electric dipoles—through the coupling between the electron and proton degrees of freedom.

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