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The search for superconductors with high values of the critical temperature has started shortly after the first observation of the phenomenon in 1911. At present, there are several paths towards reaching this goal. Here we focus on the direction based on observing high temperature superconducting state in some metallic nanoclusters. The macroscopic high Tc superconducting current can be provided by the Josephson tunneling between such clusters.

The discovery of H3S and LaH10 is an important step towards the development of room temperature superconductors which fuels the enthusiasm for finding promising superconductors among hydrides at high pressure. In the present study, three new and stable stoichiometric MoH5, MoH6 and MoH11 compounds were found in the pressure range of 100–300 GPa. The highly hydrogen-rich phase of Cmmm-MoH11 has a layered structure that contains various forms of hydrogen: H, H2− and H3− units. It is a high-Tc material with an estimated Tc value in the range of 165–182 K at 250 GPa. The same structures are also found in NbH11, TaH11, and WH11, each material showing Tc ranging from 117 to 168 K. By combining the method of using two coupling constants λopt and λac, and two characteristic frequencies (optical and acoustic) with first-principle calculations, we found that the high values of Tc are mainly caused by the presence of high frequency optical modes, but the acoustic modes also play a noticeable role.

Our paper is concerned with the specific hydrogen compound MoH

Hydrogen-based superconductors provide a route to the long-sought goal of room-temperature superconductivity, but the high pressures required to metallize these materials limit their immediate application. For example, carbonaceous sulfur hydride, the first room-temperature superconductor, can reach a critical temperature (Tc) of 288 K only at the extreme pressure of 267 GPa. The next recognized challenge is the realization of room-temperature superconductivity at significantly lower pressures. Here, we propose a strategy for the rational design of high-temperature superconductors at low pressures by alloying small-radius elements and hydrogen to form ternary hydride superconductors with alloy backbones. We identify a hitherto unknown fluorite-type backbone in compositions of the form AXH8, which exhibit high temperature superconductivity at moderate pressures. The Fm-3m phase of LaBeH8, with a fluorite-type H-Be alloy backbone, is predicted to be metastable and superconducting with a Tc ~ 191 K at 50 GPa; a substantially lower pressure than that required by the geometrically similar clathrate hydride LaH10 (170 GPa). Our approach paves the way for finding high-Tc ternary hydride superconductors at conditions close to ambient pressures., 11 pages, 4 figures

This chapter outlines the story of superconductivity, which started at the beginning of the twentieth century, and describes major breakthroughs, such as the discovery of the Meissner effect and the isotope effect. Several important developments preceded the microscopic theory formulated by Bardeen, Cooper, and Schrieffer: the two-fluid model, London equations, and the Ginzburg–Landau theory. Formulation of the theory brought further progress, such as quasiparticle tunnelling and the Josephson effect, and the search for new mechanisms of superconductivity and novel materials such as high-Tc oxides and hydrides. The main excitations in normal solids, including phonons, polaronic states, plasmons, and magnons, are described. A rigorous description of the adiabatic method, the foundation of the theory of solids, is provided, and the electron–phonon interaction, renormalisation phenomena, and the dynamic polaronic effect are introduced. The Heisenberg model, the key ingredient of the theory of magnetism, is also described.

This chapter describes the properties of a number of interesting superconducting materials. The study of phonon-mediated superconductors, such as A-15 materials and MgB2, flourished after the discovery of the high-Tc hydrides. At present, this family displays, under high pressure, record values of Tc close to room temperature. Other interesting systems, such as pnictides, heavy fermions, and ruthenates, with their peculiar interplay of superconductivity and magnetism, are also described. Fe-based superconductors, which were recently discovered, have relatively high Tc at ambient pressure. They display a two-gap energy spectrum. Pairing in intercalated nitrides is mainly provided by acoustic plasmons. Tungsten oxides represent a new family of oxides containing elements other than copper; they form filamentary structures. A special class is formed by topological superconductors; usually their properties are caused by odd-parity pairing. The presence of the states inside of the energy gap make these superconductors similar to topological insulators.

This chapter discusses superconducting states in nature. The absence of resistance is the most remarkable manifestation of the superconducting state. But pair correlation is a general phenomenon that can be manifested in various systems, such as atomic nuclei, where the pairing is manifested in spectra, especially via the odd–even effect (the presence of unpaired nucleons makes it possible for nuclei to absorb a lower frequency of radiation than nuclei with an even number of nucleons can) and in the amplitudes of their momenta of inertia, which are smaller than in a rigid model. Another system, the neutron star, has an entirely different spatial scale. However, its low heat capacity leads to its rapid cooling, and the existence of a vortex structure affects the star’s rotation period. Finally, biologically active systems contain delocalised electrons, and the formation of electron pairs affects charge transfer, which is similar to Josephson tunnelling.

This chapter focuses on manganites. There is a large similarity between the two families of mixed-valence compounds, the cuprates and the manganites. However, manganites display colossal magnetoresistance. The most fundamental property of manganites is the strong correlation between their transport properties and their magnetic properties. This correlation is caused by the double-exchange mechanism. The Hund interaction and the Jahn–Teller effect are the key ingredients of the microscopic theory. The transition to the ferromagnetic and metallic state is of a percolative nature. The superconducting–antiferromagnetic–superconducting Josephson junction is described. One can observe giant oscillations of the Josephson current as a function of a weak external magnetic field. The main properties, including the electron–hole asymmetry can be described in the framework of a generalised two-band picture. A peculiar isotope effect can be observed.

This chapter focuses on the cuprates, which are uniquely interesting superconducting compounds due to their high Tc, peculiar properties, and potential for applications. The history of the discovery of this very unusual class of superconductors is described, together with the properties and key theoretical concepts that can be used to understand their superconducting and normal behaviours. This chapter contains a description of some very key aspects of these materials: their very unusual phase diagram, where doping takes the compounds from antiferromagnetic insulators to high-temperature superconductors and finally to metallic conductivity; their very anomalous upper critical field Hc2; the symmetry of their order parameter; and the unusual isotope effect on Tc and penetration depth. There are two main approaches to the issue of the origin of high Tc in the cuprates: the phonon mechanism, with the strong impact of the polaronic effect, and a mechanism based on strong correlation effects.

In this chapter, several of the most important experimental techniques are described. These have been used to probe the most fundamental properties of the superconducting state: the energy gap and the pairing interaction. These methods have played a crucial role in validating the mechanism of superconductivity in conventional superconductors and are key to a fundamental understanding of superconductivity in more recently discovered novel superconductors like cuprates, Fe-based superconductors, and so on. The techniques that are described are all spectroscopic: tunnelling of quasiparticles through an insulating barrier or through a point contact ,Josephson tunnelling, the interaction of photons with a superconducting film or surface, the attenuation of ultrasonic waves,, the relaxation and/or resonance of muons interacting with a superconducting compound, and resonant inelastic X-ray scattering (RIXS). High-pressure techniques and the preparation of thin films and junctions are described. In addition, a state-of-the-art experimental procedure that enables the observation of the Little mechanism is discussed.

This chapter focuses on the spectroscopy of the superconducting state. Various manifestations of macroscopic quantisation are described, including flux quantisation, the Josephson effect, vortices, and the Little–Parks effect. The Ginzburg–Landau theory and its microscopic derivation are presented. An interesting new direction, the search for the lossless ground current state, undergoes an intensive development. If the electronic density of states contains several peaks, it manifests as a multigap structure. Impurity scattering and, especially, the pair-breaking effect can drastically affect the spectrum and lead to gapless superconductivity. Pairing can be induced by the proximity effect (S–N contact). The isotope effect is the signature of the pairing mechanism, but it can be affected by Coulomb terms, magnetic impurities, and polaron formation. The study of fluctuations forms a large area of research. Fluctuations affect the behaviour of heat capacity and nuclear magnetic resonance relaxation, lead to peculiar paraconductivity, and so on.

The discovery of H

The high critical temperature phase of lanthanum hydrides deserves special attention because this phase displays the highest observed critical temperature. We focus on the evaluation of the critical temperature, isotope coefficient, and their pressure dependence of this phase (Fm3m phase of the LaH10 compound). By combining the method of two coupling constants, describing the interaction with the optical and acoustic modes, and two characteristic frequencies with first-principle calculations we are able to analyze the role of the light hydrogen in the amplitude of the critical temperature in this unique compound. Specifically, the critical temperature of 254 K and the isotope coefficient of 0.45 are evaluated at high pressure, and the results are in good agreement with the experimental data. The peculiar decrease in the value of the critical temperature upon further increase in pressure is explained by the presence of a flat region on the Fermi surface and the appearance of a two-gap structure, which should be experimentally observable by tunneling spectroscopy., 21 pages, 6 figures,2 tables

Phonon spectrum of many superconducting compounds and, especially, high Tc hydrides, is broad and rather complicated ,because of presence of high frequency optical modes. In order to analyze an interplay of optical and acoustic phonon branches,it is convenient to introduce two coupling constants, {\lambda}opt. and {\lambda}ac., along with to characteristic frequencies. The correlation between the value of Tc with this interplay is demonstrated for the family of tantal hydrides (TaH2/ TaH4/ TaH6). The problem of upper limit of Tc is discussed. The phenomenon of room temperature superconductivity can be provided by the electron-phonon interaction and described by the strong coupling theory., Comment: 15 pages,1 figure,1 table

Sulfur and lanthanum hydrides under compression display superconducting states with high observed critical temperatures. It has been recently demonstrated that carbonaceous sulfur hydride displays room temperature superconductivity. However, this phenomenon has been observed only at very high pressure. Here, we theoretically search for superconductors with very high critical temperatures, but at much lower pressures. We describe two of such sodalite-type clathrate hydrides, YbH6 and LuH6. These hydrides are metastable and are predicted to superconduct with T c ∼ 145 K at 70 GPa and T c ∼ 273 K at 100 GPa, respectively. This striking result is a consequence of the strong interrelationship between the f states present at the Fermi level, structural stability, and the final T c value. For example, TmH6, with unfilled 4f orbitals, is stable at 50 GPa, but has a relatively low value of T c of 25 K. The YbH6 and LuH6 compounds, with their filled f-shells, exhibit prominent phonon “softening”, which leads to a strong electron-phonon coupling, and as a result, an increase in T c.

Superconducting state at room temperature is a perfectly realistic phenomenon, and there are various paths aimed at reaching this goal. Some of them are described briefly in this presentation. One can expect that the first breakthrough will occur with the use of the high-pressure methods. An external pressure is the thermodynamic parameter, and its change allows one to create new structures, including that of sulfur hydride displaying the record value of the critical temperature.

Remarkable feature of the phase diagram of sulfur hydrides, the record-high T c superconductors, is a sharp increase near P ≈ 150 GPa from T c ≈ 120 to ≈ 200 K. This increase is a signature of the structural transition. The present study is concerned with the nature of this phase transition. One can demonstrate that the symmetry analysis along with an analysis of the impact of lattice deformations lead to the conclusion that we are dealing with the first-order transition. Such a transition is manifested in an abrupt appearance of small pockets on the Fermi surface and, correspondingly, the two-gap energy spectrum.

The recent discovery of H_{3}S and LaH_{10} superconductors with record high superconducting transition temperatures T_{c} at high pressure has fueled the search for room-temperature superconductivity in the compressed superhydrides. Here we introduce a new class of high T_{c} hydrides with a novel structure and unusual properties. We predict the existence of an unprecedented hexagonal HfH_{10}, with remarkably high value of T_{c} (around 213-234 K) at 250 GPa. As concerns the novel structure, the H ions in HfH_{10} are arranged in clusters to form a planar "pentagraphenelike" sublattice. The layered arrangement of these planar units is entirely different from the covalent sixfold cubic structure in H_{3}S and clathratelike structure in LaH_{10}. The Hf atom acts as a precompressor and electron donor to the hydrogen sublattice. This pentagraphenelike H_{10} structure is also found in ZrH_{10}, ScH_{10}, and LuH_{10} at high pressure, each material showing a high T_{c} ranging from 134 to 220 K. Our study of dense superhydrides with pentagraphenelike layered structures opens the door to the exploration of a new class of high T_{c} superconductors. Published version

Metallic nanoclusters and aromatic molecules are nano systems which display pair correlation similar to that in usual superconductors. Metallic clusters contain delocalized electrons whose states form energy shells similar to those in atoms or nuclei. Under special but perfectly realistic conditions, superconducting pairing in metallic nanoclusters is very strong. For realistic sets of parameters one can expect a high value of T c ( 150 K); in principle, it is possible to raise T c up to room temperature. Electrons in aromatic molecules form a two-dimensional finite Fermi system and also can display phenomena caused by pair correlation.

Even after three decades of development, high-temperature superconductivity remains one of the most challenging theoretical and experimental areas in condensed matter physics. In this Colloquium some new discoveries in this area are reviewed and possible routes toward much higher transition temperatures are analyzed.

The paper discusses fundamentals of record-TC superconductivity discovered under high pressure in sulfur hydride. The rapid increase of TC with pressure in the vicinity of Pcr ≈ 123GPa is interpreted as the fingerprint of a first-order structural transition. Based on the cubic symmetry of the high-TC phase, it is argued that the lower-TC phase has a different periodicity, possibly related to an instability with a commensurate structural vector. In addition to the acoustic branches, the phonon spectrum of H3S contains hydrogen modes with much higher frequencies. Because of the complex spectrum, usual methods of calculating TC are here inapplicable. A modified approach is formulated and shown to provide realistic values for TC and to determine the relative contributions of optical and acoustic branches. The isotope effect (change of TC upon Deuterium for Hydrogen substitution) originates from high frequency phonons and differs in the two phases. The decrease of TC following its maximum in the high-TC phase is a sign of intermixing with pairing at hole-like pockets which arise in the energy spectrum of the cubic phase at the structural transition. On-pockets pairing leads to the appearance of a second gap and is remarkable for its non-adiabatic regime: hydrogen mode frequencies are comparable to the Fermi energy.

We show that a large transport current can flow through superconducting nets composed of nano-clusters. Although thermal and quantum fluctuations lead to a finite value of dissipation, this value can be very small in one- and two-dimensional systems for realistic parameters of the nanoclusters and distances between them. The value of the action for vortex tunneling at zero temperature can be made sufficiently large to make the dissipation negligibly small. We estimate the temperature T0 of the transition from the thermal activation to quantum tunneling.

Doped cuprates are inhomogeneous superconductors. The concept of an intrinsic critical temperature, \(T_{c}^{\mathrm{intr.}} \equiv T_{c}^{*}\), whose value greatly exceeds that for the resistive \(T_{c}^{\mathrm{res.}}\equiv T_{c}\), is supported by a number of experimental studies, including those performed recently. These data are discussed in this review. The anomalous diamagnetism observed at \(T_{c}^{\mathrm{res.}}

A general expression is derived for the Josephson current between nanoclusters. It is shown that, in the resonance conditions between electron levels of clusters, the expression for the current obtained in the tunnel Hamiltonian model becomes invalid. In the case of degeneracy or close to degeneracy of energy levels in isolated clusters, the critical Josephson current may exceed the value obtained in the model of tunnel Hamiltonian in the large parameter, viz., the ratio of the order parameter |Δ| to the distance between the resonance level and the levels closest to it.

The crystal lattice of a complex compound may contain a subsystem of ions with each one possessing two close equilibrium positions (double-well structure). For ex- ample, the oxygen ions in the cuprates form such a subsys- tem. In such a situation it is impossible to separate electronic and local vibrational motions. This leads to a large increase in the effective strength of the electron-lattice interaction, which is beneficial for pairing.

An adiabatic theory of polyatomic photodissociation is developed that explicitly treats the interaction between the relative and internal motion and leads to an expression for the nuclear wavefunction of the final dissociative state which differs considerably from the zeroth-order distorted-wave approximation. The vibrational frequencies ..omega../sub i/ of the fragments are found to depend on the interfragment distance. In the evaluation of the matrix element needed to describe the energy distribution of the fragments, it is found necessary to use values of ..omega../sub i/ different from the frequencies of the free fragments. These values of ..omega../sub i/ can be expressed in terms of the force constants of the precursor system. Inverse vibrational distributions are obtained from this theory in accord with recent experimental data.

A new version of adiabatic theory enabling one to evaluate higher-order nonadiabatic terms has been developed. One introduces a nonadiabatic Hamiltonian Ĥna so that the total Hamiltonian is given by Ĥ = Ĥ0 + Ĥna, where Ĥ0 describes the noninteracting electronic and nuclear subsystems, and Ĥna describes the electronic-vibrational coupling. The correction to the total energy is calculated. The theory is applied to vibrational Raman scattering of aromatic molecules. Nonadiabaticity is found to play a key role in vibrational Raman scattering.

In relation to the recently intensified search for new superconducting systems, it is interesting to study the properties of metal nanoclusters containing ≈102–103 free carriers. It is essential that the spectra of delocalized electrons in many clusters form energy shells similar to those in atoms and nuclei. The superconducting pairing can be very strong if the cluster parameters satisfy certain conditions. Such clusters constitute a new family of high-temperature superconductors (with Tc ≥ 150 K). Transition into the superconducting state is manifested in an essential rearrangement of the energy spectrum. Pair correlation affects the optical, magnetic, and thermodynamic properties of clusters; corresponding changes can be detected in specific experiments. Clusters can form high-temperature superconducting tunneling networks, and this leads to macroscopic high-temperature superconductivity. In principle, higher values of Tc, up to room temperature, may be achieved.

Heat capacities measured for Al 45 − and Al 47 − nanoclusters have reproducible jumps at ∼200 K. These jumps are consistent with theoretical predictions that some clusters with highly degenerate electronic states near the Fermi level will undergo a transition into a high T C superconducting state. An analysis based on a theoretical treatment of pairing in Al 45 − and Al 47 − agrees well with the experimental data in both the value of the critical temperature and in the size and width of the jumps in the heat capacity.

Novel superconducting compounds such as the high Tc oxides are intrinsically inhomogeneous systems. An inhomogeneous structure is created by doping and the statistical nature of the distribution of dopants. Consequently, the critical temperature is spatially dependent: Tc = Tc (r)., Comment: 63 pages text, 13 figures and 1 table

The electronic shell structure in small metallic nanoclusters leads to high level degeneracy, which is strongly beneficial for the appearance of pair correlation. This results in a high value of Tc as well as in the appearance of a superconducting gap which causes a strong modification of the energy spectrum. The electronic energy spectrum becomes strongly temperature dependent. Consequently, specific experiments to demonstrate the presence of pair correlation can be proposed.

The study of manganites has been undergoing intensive development, especially following the discovery of colossal magnetoresistance (CMR). The most fundamental property of these materials is a strong correlation between their transport and magnetic properties. A transition to the ferromagnetic (and metallic) state occurs at a finite doping level and represents a special type of transition which should be described in terms of percolation theory. The same applies for the transition at the Curie temperature. As a result of the percolation theory approach, the view of these materials, both above and below the transition point, is that of inhomogeneous media consisting of tiny islands of interweaving sub-phases. These basic ideas have been now verified experimentally by neutron data, X-ray analysis, Mossbauer spectroscopy, heat capacity and magnetization measurements, etc. The phase diagram as a function of doping displays a peculiar electron-hole asymmetry; this asymmetry as well as other features (e.g., the optical properties) can be explained in the framework of a generalized two-band picture. We trace how the ground state evolves with doping and give a self-consistent analysis of various thermodynamic, optical and transport properties of metallic manganites, isotope effect, etc. It is predicted that giant oscillations in the Josephson current of a S–AFM–S junction will occur as a function of weak external magnetic fields. The contact phenomena are also described.

The relaxation of an electron excited to the high energy region, is accompanied by the creation of various excitations (plasmons, quasi-particles, phonons). The stages of this many-body, non-stationary phenomenon (cascade) are described microscopically. The electron distribution function n(ɛ, t) and characteristic times for the whole energy range, are calculated.

Intercalating polyatomic molecules into a superconductor strongly modifies its superconducting properties. A mechanism for a large increase in T c is proposed that explains recent experimental findings on C60/CHX3 (X=Cl, Br, I) . The increase of T c upon intercalation as well as upon Cl→Br substitution is described in terms of the additional contribution to pairing interaction arising from the coupling of holes (or electrons) to the vibrational manifold of the intercalated haloform molecules. We also present first optimization of the crystal structure and calculations of the band structure for neutral C60/CHCl3 .

Intercalation of polyatomic molecules into a superconductor can drastically affect the properties of the compound. A mechanism leading to a large increase in Tc for such systems is proposed. It explains the recent remarkable observation of high Tc superconductivity in the hole-doped C60/CHX3 (X=Cl,Br) compounds and the large shift in their Tc upon Cl->Br substitution. The increase in Tc is due to contribution to the pairing arising from the interaction of electrons with the vibrational manifold of the molecule. The proposed mechanism opens up the possibility to observe a site-selective isotope effect. We also suggest that intercalating CHI3 would further increase the critical temperature to Tc=140K., Final expanded version of cond-mat/0109553 and cond-mat/0110327 with Journal reference

Josephson currents through an antiferromagnetic barrier are studied. The case of the spin-valve structure when the barrier is formed by ferromagnetic layers ordered antiferromagnetically in the direction perpendicular to the current (the A-structure) turns out to be most interesting. The current can be controlled and even switched off by an external magnetic field. A most remarkable feature is appearance of rapid oscillations in the current amplitudes as a function of the field.

Intercalating polyatomic molecules into a superconductor can noticeably affect the properties of the compound. We propose a mechanism leading to a large increase in Tc for such systems. The enhancement of Tc is related to the additional pairing interaction arising from the interaction of electrons with the vibrational manifold of the molecules. One immediate prediction of the model is the possibility to observe a site-selective isotope effect. The proposed mechanism explains the recent observation of high-Tc superconductivity in hole-doped intercalated fullerides. The value of Tc for the C60 ⋅ 2 CHBr3 compound is calculated withouth any adjustable parameter. The theory also suggests that intercalating CHI3 would further increase the critical temperature to Tc ≃ 140 K.

This paper describes a novel method to increase the resistive Tc of cuprate superconductors to values approaching room temperature. The method is based on our analysis of the inhomogeneous superconducting state for the “pseudogap” region and on the interplay of doping and pair-breaking phenomena. What we propose involves specific ordering of the dopants that leads to the formation of regions that can carry a supercurrent at high temperatures.

Electronic states in metallic nanoclusters form energy shells and degree of their filling depends on the number of delocalized electrons. In the region close to half-filling the cluster's geometry oscillates between the prolate and oblate configurations (dynamic Jahn-Teller effect). For large clusters ( N > 10 2 ; N is the number of delocalized electrons) this effect competes with pair correlation and, as a result, it is perfectly realistic to observe the transition to the superconducting state. For some clusters ( e.g. , for Zn 76 , Al 70 ) the value of the critical temperature is rather high .