New superconductivity dome in LaFeAsO1−xFx far away from magnetism and accompanied by structural transition

We report on the discovery and novel physics of a new superconductivity dome in LaFeAsO_1?xF_x with high-doping rate (0.25 ≤x≤0.75) synthesized by using the high-pressure technique. The maximal critical temperature T_c = 30 K peaked at x_opt = 0.5 ～0.55, which is even higher than that at x≤ 0.2. By nuclear magnetic resonance (NMR), we find that the new superconducting dome is far away from a magnetically ordered phase without low-energy magnetic fluctuations. Instead, NMR and transmission electron microscopy measurements indicate that a C4 rotation symmetry-breaking structural transition takes place for x> 0.5 above T_c. The electrical resistivity shows a temperature-linear behavior around the doping level where the crystal transition temperature extrapolate to zero and T_c is the maximal, suggesting the importance of quantum fluctuations associated with the structural transition. Our results point to a new paradigm of high temperature superconductivity.     

Magnetic phase diagram and correlation between metamagnetism and superconductivity in Ru<Subscript>0.9</Subscript>Sr<Subscript>2</Subscript>YCu<Subscript>2.1</Subscript>O<Subscript>7.9</Subscript>

The magnetic superconductorRu_0.9Sr₂YCu_2.1O_7.9 (Ru-1212Y) has beeninvestigated using neutron diffraction under variable temperature and magnetic field. Withthe complementary information from magnetization measurements, we propose a magnetic phasediagram T-H for the Ru-1212 system. Uniaxialantiferromagnetic (AFM) order of 1.2μ _B /Ruatoms with moments parallel to the c-axis is found below the magnetictransition temperature at  ~140 K in the absence of magnetic field. In addition,ferromagnetism (FM) in the ab-plane develops below  ~120 K, butis suppressed at lower temperature by superconducting correlations. Externally appliedmagnetic fields cause Ru-moments to realign from the c-axis to theab-plane, i.e. along the ?1,1,0? direction, and induce ferromagnetismin the plane with  ~1μ _B at 60 kOe.These observations of the weak ferromagnetism suppressed by superconductivity and thefield-induced metamagnetic transition between AFM and FM demonstrate not only competingorders of superconductivity and magnetism, but also suggest a certain vortex dynamicscontributing to these magnetic transitions.     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.     

Magnetism and superconductivity in Eu(Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ni<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)As<Subscript>2</Subscript> (<Emphasis Type="Italic">x</Emphasis> = 0, 0.04)

We report Eu-local-spin magnetism and Ni-doping-induced superconductivity (SC) in a 112-type ferroarsenide system Eu(Fe_1?xNi_x)As₂. The non-doped EuFeAs₂ exhibits two primary magnetic transitions at ~100 and ~40 K, probably associated with a spin-density-wave (SDW) transition and an antiferromagnetic ordering in the Fe and Eu sublattices, respectively. Two additional successive transitions possibly related to Eu-spin modulations appear at 15.5 and 6.5 K. For the Ni-doped sample with x = 0.04, the SDW transition disappears, and SC emerges at T_c = 17.5 K. The Eu-spin ordering remains at around 40 K, followed by the possible reentrant magnetic modulations with enhanced spin canting. Consequently, SC coexists with a weak spontaneous magnetization below 6.2 K in Eu(Fe_0.96Ni_0.04)As₂, which provides a complementary playground for the study of the interplay between SC and magnetism.     

Unconventional superconductivity

‘Conventional’ superconductivity, as used in this review, refers to electron–phonon-coupled superconducting electron pairs described by BCS theory. Unconventional superconductivity refers to superconductors where the Cooper pairs are not bound together by phonon exchange but instead by exchange of some other kind, e.g. spin fluctuations in a superconductor with magnetic order either coexistent or nearby in the phase diagram. Such unconventional superconductivity has been known experimentally since heavy fermion CeCu₂Si₂, with its strongly correlated 4f electrons, was discovered to superconduct below 0.6?K in 1979. Since the discovery of unconventional superconductivity in the layered cuprates in 1986, the study of these materials saw T_c jump to 164?K by 1994. Further progress in high-temperature superconductivity would be aided by understanding the cause of such unconventional pairing. This review compares the fundamental properties of 9 unconventional superconducting classes of materials – from 4f-electron heavy fermions to organic superconductors to classes where only three known members exist to the cuprates with over 200 examples – with the hope that common features will emerge to help theory explain (and predict!) these phenomena. In addition, three new emerging classes of superconductors (topological, interfacial – e.g. FeSe on SrTiO₃, and H₂S under high pressure) are briefly covered, even though their ‘conventionality’ is not yet fully determined.     

Study of the heavy-fermion compound CeRu<Subscript>2</Subscript>Si<Subscript>2</Subscript> by the small-angle neutron scattering method

In order to directly observe neutron scattering by heavy fermion quasiparticles at low temperatures, a CeRu₂Si₂ single crystal has been studied by the small-angle neutron scattering method. In the experiment, neutron scattering is observed at T = 0.85 K for momentum transfers q ≤ 0.04 Å^?1, which is treated as the orbital component of magnetic scattering by heavy fermion quasiparticles. It has been found that the application of a magnetic field H = 1 T leads to both an increase in the observed scattering and its anisotropy with respect to the field direction. Moreover, measurements in the magnetic field reveal additional scattering for q > 0.04 Å^?1, which is well described by a Lorentzian and is interpreted as neutron magnetic scattering by spin-density fluctuations with a correlation radius R_c ≈ 30 Å.     

Theory of dual fermion superconductivity in hole-doped cuprates

Since the discovery of the cuprate high-temperature superconductivity in 1986, a universal phase diagram has been constructed experimentally and numerous theoretical models have been proposed. However, there remains no consensus on the underlying physics thus far. Here, we theoretically investigate the phase diagram of hole-doped cuprates based on an itinerant-localized dual fermion model, with the charge carriers doped on the oxygen sites and localized holes on the copper d _{x2 ? y2} orbitals. We analytically demonstrate that the puzzling anomalous normal state or the strange metal could simply stem from a free Fermi gas of carriers bathing in copper antiferromagnetic spin fluctuations. The short-range high-energy spin excitations also act as the “magnetic glue” of carrier Cooper pairs and induce d-wave superconductivity from the underdoped to overdoped regime, distinctly different from the conventional low-frequency magnetic fluctuation mechanism. We further sketch out the characteristic dome-shaped critical temperature T _c versus doping level. The emergence of the pseudogap is ascribed to the localization of partial carriers coupled to the local copper moments or a crossover from the strange metal to a nodal Kondo-like insulator. Our work provides a consistent theoretical framework to understand the typical phase diagram of hole-doped cuprates and paves a distinct way to the studies of both non-Fermi liquid and unconventional superconductivity in strongly correlated systems.     

Surface and volume superconductivity of Pb embedded in nanopores

The heat capacity of lead embedded in glass nanopores (7 nm in diameter) and bulk lead was studied in the temperature range 2–40 K without a magnetic field and in magnetic fields of 1–8 T. The properties of lead nanoparticles and bulk lead were compared. The results obtained allowed us to separate the surface superconductivity from the volume superconductivity. The temperature dependence of the heat capacity of lead nanoparticles was shown to exhibit two superconducting transitions above and below the transition temperature for bulk lead (T _c = 7.2 K), which are associated with the surface and volume superconductivity. The upper critical fields H _c3 for the surface superconductivity and H _c2 for the volume superconductivity were determined. It turned out that these fields for Pb nanoparticles are two orders of magnitude higher than those for bulk lead. The “superconductor-normal metal” phase diagrams were constructed for lead nanoparticles. The study established an increase in the density of low-frequency excitations in Pb nanocrystals as compared to bulk Pb and a difference in the electronic heat capacity of Pb nanoparticles as compared to bulk Pb.     

Structural and magnetic properties of CeZnAl<Subscript>3</Subscript> single crystals

We have synthesized single crystals of CeZnAl₃, which is a new member of family of Ce-based intermetallics CeTX₃ (T=transition metal, X=Si, Ge, Al), crystallizing in the non-centrosymmetric tetragonal BaNiSn₃-type structure. Magnetization, specific heat and resistivity measurements all show that CeZnAl₃ orders magnetically below around 4.4 K. Furthermore, magnetization measurements exhibit a hysteresis loop at low temperatures and fields, indicating the presence of a ferromagnetic component in the magnetic state. This points to a different nature of the magnetism in CeZnAl₃ compared to the other isostructural CeTAl₃ compounds. Resistivity measurements under pressures up to 1.8 GPa show a moderate suppression of the ordering temperature with pressure, suggesting that measurements to higher pressures are required to look for quantum critical behavior.     

Magnetism in structures with ferromagnetic and superconducting layers

The influence of superconductivity on ferromagnetism in the layered Ta/V/Fe_1–x V _x /V/Fe_1–x V _x /Nb/Si structures consisting of ferromagnetic and superconducting layers is studied using polarized neutron reflection and scattering. It is experimentally shown that magnetic structures with linear sizes from 5 nm to 30 μm are formed in these layered structures at low temperatures. The magnetization of the magnetic structures is suppressed by superconductivity at temperatures below the superconducting transition temperatures in the V and Nb layers. The magnetic states of the structures are shown to undergo relaxation over a wide magnetic-field range, which is caused by changes in the states of clusters, domains, and Abrikosov vortices.     

Superconducting Properties of Indium Nanostructured in Pores of Thin Films of SiO<Subscript>2</Subscript> Microspheres

Samples of a superconducting indium nanocomposite based on a thin-film porous dielectric matrix prepared by the Langmuir–Blodgett method are obtained for the first time, and their low-temperature electrophysical and magnetic properties are studied. Films with thickness b ≤ 5 μm were made from silicon dioxide spheres with diameter D = 200 and 250 nm; indium was introduced into the pores of the films from the melt at a pressure of P ≤ 5 kbar. Thus, a three-dimensional weakly ordered structure of indium nanogranules was created in the pores, forming a continuous current-conducting grid. Measurements of the temperature and magnetic field dependences of the resistance and magnetic moment of the samples showed an increase in the critical parameters of the superconductivity state of nanostructured indium (critical temperature T_c ≤ 3.62 K and critical magnetic field H_c at T = 0 K H_c(0) ≤ 1700 Oe) with respect to the massive material (T_c = 3.41 K, H_c(0) = 280 Oe). In the dependence of the resistance on temperature and the magnetic field, a step transition to the superconductivity state associated with the nanocomposite structure was observed. A pronounced hysteresis M(H) is observed in the dependence of the magnetic moment M of the nanocomposite on the magnetic field at T < T_c, caused by the multiply connected structure of the current-conducting indium grid. The results obtained are interpreted taking into account the dimensional dependence of the superconducting characteristics of the nanocomposite.     

Magnetism and superconductivity in a quasi-2D anisotropic system doped with charge carriers

The theory of multiband superconducting systems with variable density of charge carriers is analyzed. The possibility of emergence of nonphonon high-temperature superconductivity due to the predominance of electron–electron interband interactions over intraband interactions, as well as due to the fact that the thermodynamic and magnetic properties of multiband systems in the superconducting phase differ qualitatively from those of single-band systems, is indicated. Phase transitions in a quasi-2D anisotropic medium upon a change in the carrier concentration, i.e., a transition from the commensurate to the incommensurate state of the spin density wave, are analyzed. Such a transition is observed when the Umklapp processes in the lattice structure are taken into account. These processes facilitate a deviation of wavevector Q of the spin density wave from 2k_F, as well as a displacement of the bandgap relative to the Fermi surface. This leads to the generation of free charge carriers and the possibility of superconductivity. It is shown that superconductivity accompanies the magnetism. The conditions for the coexistence of these two phenomena are determined.     

The competition and coexistence of antiferromagnetism and <Emphasis Type="Italic">d</Emphasis>-wave superconductivity: probing coupled thermal fluctuations in a two dimensional minimal model

We consider the coexistence of antiferromagnetism and d-wave superconductivity, motivated by what one observes in the quasi-two dimensional organic salts. We study an electronic model that approximates some features of the Hubbard model, e.g., a repulsion that promotes local moments and Neel order, and an attractive intersite density–density coupling that promotes d-wave superconductivity. Staying at half-filling and a fixed attractive interaction we probe the effect of varying repulsion, using mean field theory for the ground state but retaining the full O(3) × U(1) spectrum of classical fluctuations at finite temperature. The ground state is superconducting at weak repulsion, a Neel ordered insulator at large repulsion, and a coexistence of the two orders in the intermediate regime. We observe four distinct kinds of thermal behaviour depending on the strength of repulsion. Starting with weak repulsion these are, first, a d-wave superconductor renormalised by magnetic fluctuations, second, a d-wave state transiting to an antiferromagnetic insulator and then to the normal state, third, a coexistent state transiting to the antiferromagnetic insulator and then the normal state, and, fourth, a Neel ordered insulator with weak pairing fluctuations. The low temperature state is either “nodal” or gapped, due to long range order, and the low energy spectral weight generally increases monotonically with temperature. At intermediate repulsion, however, the transition from the d-wave state to Neel antiferromagnet causes a loss of low energy weight which is gradually regained only at high temperature.     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.     

Ground state pairing correlation competes in the doped triangular lattice Hubbard model

By using the constrained path quantum Monte carlo method, we study the ground state paring correlations in the t ? U ? V Hubbard model on the triangular lattice. It is shown that pairings with various symmetries dominate in different electron filling regions. The pairing correlation with fn-wave symmetry dominates over other pairings around half fillings, and as the electron filling decreases away from the half filling, the d + id-wave pairing correlation tends to dominate. As the electron filling is bellow the Van Hove singularity, the f-wave pairing dominates. These crossovers are due to the interplay of electronic correlation and geometric frustration, associating with the competition between the antiferromagnetic correlations and ferromagnetic fluctuations. Our findings reveal the possible magnetic origin of superconductivity, and also provide useful information for the understanding of superconductivity in Na _x CoO₂·H₂O and the organic compounds.     

Interplay between the magnetic fluctuations and superconductivity in lanthanum cuprates

We report an analysis of the magnetic fluctuations in superconducting La_2?xSr_xCuO₄ and related lanthanum cuprates that have different symmetry of the low-temperature structure. NMR and ESR investigations revealed a dynamical coexistence of superconductivity and the antiferromagnetic correlations in most of the superconductivity region of the phase diagram. We show that, for all compounds, regardless of their low-temperature symmetry and their superconducting properties, the enhancement of the spin stiffness near 1/8 doping takes place.     

Emergence of F(R) gravity-analogue due to defects in graphene

We show that the defects of graphene, which lead to the non-equality between positive curvature of fermions with anti-parallel spins and negative curvature of fermions with parallel spins, imply an emergence of F(R) gravity. By increasing the number of atoms at each defect, the order of scalar curvature increases and the shape of F(R) gravity changes. This gravity has a direct relation with energy-momentum tensor and leads to motion of electrons in a special path and hence producing superconductivity. Also, for some special angles, parallel spins become close to each other and repel to each other. In that condition, the shape of F(R) gravity changes and electrons can’t continue to move in an initial path and return. Consequently, superconductivity disappears and one new conductivity appears in opposite direction.     

Topological superconductivity and the fractional Josephson effect in quasi-one dimensional wires on a plane

A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one-dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin–orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of the Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle–hole symmetry. Tunneling of Majorana quasiparticle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with 4π-periodicity.     

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.     

New kinds of superconductivity and superfluidity

Formation of self-organized macroscopic and periodic structures in a physical system of interacting fermions are derived from first principles. The system of structureless and chargeless fermions with magnetic moments can have four different phases. Two of these phases exhibit the totally unique phenomena typical for superconductivity and superfluidity as well as various kinds of structural singularities such as disgyrations in the superfluid ³He.