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High pressure serves as a path finding tool towards novel structures, including those with very high Tc.The superconductivity in sulfur hydrides with record value (203 K) is caused by the phonon mechanism. However, the picture differs from the conventional one in important ways. The phonon spectrum in sulfur hydride is both broad and has a complex structure. High value of Tc is mainly due to strong coupling to the high-frequency optical modes, although the acoustic phonons also make a noticeable contribution. New approach is described;it generalizes the standard treatment of the phonon mechanism and makes it possible to obtain an analytical expression for Tc . It turns out that, unlike in the conventional case, the value of the isotope coefficient varies with the pressure and reflects the impact of the optical modes. The phase diagram, that is the pressure dependence of Tc, is rather peculiar. A crucial feature is that increasing pressure results in a series of structural transitions, including the one, which yields the superconducting phase with the record Tc.In a narrow region near 150GPa the critical temperature rises sharply from 120K to 200K. The sharp structural transition, which produces the high Tc phase, is a first-order phase transition caused by interaction between the order parameter and lattice deformations.Remarkable feature of the electronic spectrum in the high Tc phase is the appearance of small pockets at the Fermi level. Their presence leads to a two-gap spectrum, which can, in principle, be observed, with the future use of tunneling spectroscopy. This feature leads to non-monotonic and strongly asymmetric pressure dependence of Tc. Other hydrides can be expected to display even higher values of Tc, up to room temperature. The fundamental challenge lays in creation a structure capable of displaying high Tc at ambient pressure., Comment: 67 pages,7 figures

Remarkable feature of the phase diagram of sulfur hydrides is a sharp increase in critical temperature from 120K up to200K. This increase is a signature of the structural transition. The study described below 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. It leads to an abrupt appearance of small pockets on the Fermi surface and to the two-gap energy spectrum., Comment: 21 pages,3 figures

We have analyzed two mechanisms proposed recently for superconductivity in doped SrTiO3 - the plasmon-mediated pairing and the potential of an instantaneous attraction between two electrons that owes its origin to the exchange by high-frequency optical phonons. The first approach seems to be self-consistent, but in a limited range of the dielectric constant. As to the direct instantaneous interaction between two electrons,it was hypothesized as due to the exchange by the band LO phonons. The latter supposition was incorrect. In the current paper, it shows that the contributions into the pairing matrix element possessing the structure of a net attraction come about only as the result of disorder. Indeed, the experiment revealed the mobility edge in doped SrTiO3. Doped electrons occupying states with the energy below the mobility edge are localized on dopants thereby become strongly coupled with the lattice vibrations. The emergence of the localized phonon modes attached to defect is one of the results of such electron-lattice coupling. For two electrons in the conduction band the virtual exchange by the quantum of such local mode manifests itself as the effective attraction. The total contribution into the pairing matrix element from these processes, increasing with concentration can overwhelm the Coulomb repulsion screened by the band LO phonons. That is, the role previously ascribed to the band LO phonons actually belongs to the localized phonons.

The rapid variation of the superconductivity Tc in hydride sulfur (H3S) under high pressure [A. Drozdov et al, Nature 525, 73 (2015); M. Einaga et al, arXiv: 1509.03156] in a vicinity Pcr=123GPa is interpreted in terms of the 1st order transition, possibly related to a CDW-instability with a non-zero structural vector. The superconductivity mechanisms in high-Tc phase be discussed, ordinary methods of calculating Tc are shown not applicable in H3S because, beside the acoustic branches, its phonon spectrum contains hydrogen modes with much higher frequency. A modified approach provides realistic Tc values. The isotope effect (change of Tc at the substitution of deuterium for hydrogen) owes its origin to the high frequency of phonons and is different in different phases. The decrease of Tc after reaching a maximum in high-T phase is due to the interaction with the second gap arising on a hole-like pocket. The phonon-mediated pairing on the latter is in a non-adiabatic regime of the frequency omega of hydrogen modes comparable to the Fermi energy., Comment: 11 pages + Supplemental Materials

Observation of replica bands in the ARPES spectra of the single-layer FeSe on strontium titanate substrate revealed a phonon component among mechanisms behind high Tc superconductivity there. We study the interaction of the in-layer FeSe electrons with the electric potential of the longitudinal (LO) modes at surface of bulk SrTiO3. A two-dimensional system of charges at the FeSe/SrTiO3 interface includes both the itinerant and immobile electrons. The latter significantly change the interface characteristics, increasing screening at the substrate surface and reducing thereby the strength of the electron-LO phonon interactions. In that follows the dielectric constant serves as a free parameter and is found from the ARPES data for the replicas. The two-dimensional Coulomb screening is accounted for in the random phase approximation. It is shown that the model is applicable within the whole range of the parameters typical for current experiments. The estimates allow concluding that the LO-phonon mediated pairing alone cannot account for the temperatures of the superconducting transition Tc in the single-layer FeSe/SrTiO3 reported in these experiments. This does not exclude that the LO-phonons mechanism can become more significant in the differently and better prepared single layer FeSe films. Available experiments are briefly discussed. Thus far no data exist on the dependence of Tc on the concentration of electrons doped into the in-layer FeSe band.

We analyze the mathematical structure of equations for temperature Tc of the superconductivity transition in a gas of interacting Fermi particles or at the phonon-mediated pairing in a metal in case of non-adiabatic conditions, i. e., when the characteristic phonon frequency is comparable or larger than the Fermi energy . The integral equations for Tc are derived in the logarithmical approximation. The equations contain no divergent terms in the anti-adiabatic limit.

Superconductivity of doped SrTiO3 is proven to be a particular case of the broader concept of the non-adiabatic pairing mediated by phonons with frequency comparable or larger the Fermi energy. We argue that, for carrier concentrations exceeding that of the mobility edge, the superconductivity of doped SrTiO3 is mediated by interaction of electrons with several longitudinal (LO) optical polar phonons. The electronic spectrum of SrTiO3 consists at low temperatures of three conduction bands which are successively doped. Each band contributes to the Cooper instability and exhibits a superconducting gap in the energy spectrum. The theory presented below predicts maxima in dependence of Tc(n)-the transition temperature on n, the number of electrons owing to the following mechanism. Doping by electrons increases density of states at the Fermi surface and Tc initially grows up. At the same time, screening on the part of accumulating charges tends to reduce amplitude of the electrical fields inherent in LO phonon modes and at larger concentrations the matrix element of interaction between electrons and LO phonons decreases. The compromise between the two tendencies leads to maxima in the Tc(n)-dependence providing interpretation to one of the most intriguing experimental findings in Xiao Lin et al [Phys. Rev. Lett. 112, 207002 (2014)]. Having reached a maximum in the third band, the superconducting transition finally decreases, rounding out the Tc(n)-dome, the three maxima in Tc(n)with accompanying superconducting gaps emerging consecutively as electrons fill successive bands. This arises from attributes of the LO optical phonon pairing mechanism. More generally, the mechanism opens prospect of increasing temperature of the superconducting transition in transition-metals oxides and other polar crystals., Comment: 5 figures

We study properties of electrons on illuminated surfaces of SrTiO3 with titanium dxz_dyz and dxy bands for their spectrum. Recently A. F. Santander-Syro et al [Nature Materials, 13, 1085 (2014)] found that the dxy bands actually comprise two chiral branches with the Kramers degeneracy at the zone center lifted in absence of a magnetic moment. From symmetry analysis of instabilities possible in the Fermi liquid with exchange interactions we identified the metallic in-layer state with the concrete antiferromagnetic phase and discuss if the same state materializes at conducting LaAlO3_SrTiO3 interfaces., Comment: 8 pages, 1 figure

N. Doiron-Leyraud et al. in [1] report on the experimental observation of small holes pockets in the energy spectrum of YBa2Cu3Oy (YBCO) coming below the transition into the charge ordered (CO) phase as a result of a Fermi surface (FS) reconstruction. We comment that their results seem to be more consistent with a unidirectional charge density wave (CDW) vector direction of which alternates along the c-axis between neighboring CuO2 -planes., Comment: 8 pages, 1 figure, some formulas are corrected, the reference list and the figure are updated

We studied interactions between the coherent excitations on disconnected arcs along a bare Fermi surface (the so-called Fermi arcs (FAs)) seen by angle-resolved photo emission spectroscopy (ARPES) in several underdoped (UD) cuprates and incommensurate charge density wave (IC CDW) ordering at lowering of the temperature., Comment: This paper has been withdrawn by the author: while Eq.(11) is correct,the estimate for the imaginary part in Eq.(15) is wrong

In the search for mechanisms of high-temperature superconductivity it is critical to know the electronic spectrum in the pseudogap phase from which superconductivity evolves. The lack of angle-resolved photoemission data for every cuprate family precludes an agreement as to its structure, doping and temperature dependence and the role of charge ordering. Here we show that, in the entire Fermi-liquid-like regime that is ubiquitous in underdoped cuprates, the spectrum consists of holes on the Fermi arcs and an electronic pocket. We argue that experiments on the Hall coefficient identify the latter as a permanent feature at doped hole concentration x>0.08-0.10, in contrast to the idea of the Fermi surface reconstruction via charge ordering. The longstanding issue of the origin of the negative Hall coefficient in YBCO and Hg1201 at low temperature is resolved: the electronic contribution prevails as mobility of the latter (evaluated by the Dingle temperature) becomes temperature independent, while the mobility of holes scattered by the short-wavelength charge density waves decreases., Comment: 16 pages, 3 figures, title changed, final manuscript, close to the published version, Scientific Reports 5, (2015)

We address recent experiments shedding light on the energy spectrum of under- and optimally doped cuprates at temperatures above superconducting transition. Angle resolved photoemission reveals coherent excitation only near nodal points on parts of the "bare" Fermi surface known as the Fermi arcs. The question debated in the literature is whether the small normal pocket, seen via quantum oscillations exists at higher temperatures or forms below a charge order transition in strong magnetic fields. Assuming the former case as possibility, expressions derived for the resistivity and the Hall coefficient (in weak and strong magnetic fields) with both types of carriers participating in transport. There are two regimes. At higher temperatures (at a fixed field) electrons are dragged by the Fermi arcs' holes. The pocket being small its contribution into conductivity and the Hall coefficient is negligible. At lower temperatures electrons decouple from holes behaving as a Fermi gas in the magnetic field. Mobility of holes on the arcs decreasing in strong fields with decrease of temperature, below a crossover point the pocket electrons prevail changing sign of the Hall coefficient in the low temperature limit. Such behavior finds its confirmation in recent high-field experiments., Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1309.0778

Angle resolved photoemission (ARPES) experiments reveal the coherent electronic excitation in the energy spectrum of under- and optimally doped cuprates at temperatures above their temperature of transition into superconducting state only near nodal points on the parts of the "bare" Fermi surface known as the Fermi arcs. That raises questions about the meaning and possible interpretations of the experimental data. Below we derive expressions for the Hall coefficient for the Fermi arc model both in weak and strong magnetic fields., Comment: 4 pages

The Fermi-liquid-like (FL) resistivity recently observed in clean HgBa2CuO4 below the pseudogap temperature was related to carriers at the nodal points on the Fermi surface [4]. We show that this necessitates important implications for the electronic spectrum of underdoped (UD) cuprates in whole. Photoemission experiments picture the spectrum as of metallic arcs separated from each other by regions with large energy gaps. We solved the kinetic equation in such model rigorously. The Fermi arcs carriers contribute to FL resistivity, if scattering between the opposite nodal points admits the Umklapp processes. The Hall coefficient defines the effective number of carriers on arcs and has the positive sign. For clean materials the expression is applicable only at weak magnetic fields. We discuss the Fermi arcs concept further in light of recent experimental findings and argue that the idea of reconstructed FS in UD cuprates is not consistent with the FL-like resistivity., Comment: Definition of charge carriers at the Fermi arcs is given. Sign of the Hall coefficient changed to be positive

In the stoichiometric Fe-pnictides the same d-electrons form the local moments and participate in the metallic conductivity. In the manuscript the emergence of the magnetic moments on the Fe-sites, their interaction with the itinerant electrons are studied in the paramagnetic phase at the different relations between the onsite Coulomb repulsion and the intraatomic Hund's exchange. The energy of the local center that is due to its interaction with the conduction electrons is calculated exactly. It is found that the spin density wave transition is controlled by the RKKY interactions between the centers rather than by the nesting mechanism. In the paramagnetic phase the electrons scatter on the randomly oriented moments. The calculated inverse mean free time provides the interpretation for few available experimental data on the conductivity. The multi-band structure of the energy spectrum in iron pnictides is taken into account., Comment: 16 pages

Dilute Nd in simple cubic LaB$_6$ shows electrical resistance and specific heat features at low temperature consistent with a Kondo scale of $T_K \lesssim$ 0.3 K. Nd has a well localized {\it 4f}$^{3}$ {\it J} = 9/2 Hund's Rule configuration which is not anticipated to be Kondo coupled to the conduction electrons in LaB$_6$. We conjecture that the unexpected Kondo effect arises via participation of {\it 4f} quadrupolar degrees of freedom of the Nd crystal field ground state quartet., Comment: 5 pages, 4 figures

We argue that the low- frequency quantum oscillations observed recently in the vortex state of underdoped ortho II-YBCO have the same origin as in other strongly correlated electronic systems. Superconductivity driven by strong interactions on several Fermi surfaces creates proximity gaps on the other. The gap transferred on a small-sized pocket from larger Fermi surfaces is small. In case of unconventional pairing symmetry the induced gap is proportional to ratio of the oscillations' frequencies for small and large Fermi surfaces. The gap is in inverse proportion to mass enhancement on the latter. We share the view that small pockets themselves are certain feature of topology of the band Fermi surfaces.

We consider single band of conduction electrons interacting with displacements of the transitional ions. In the classical regime strong enough coupling transforms the harmonic elastic energy for an ion to the one of the well with two deep minima, so that the system is described in terms of Ising spins. Inter-site interactions order spins at lower tempratures. Extention to the quantum regime is discussed. Below the CDW-transition the energy spectrum of electrons remains metallic because the structural vector Q and the FS sizes are not related. Large values of the CDW gap seen in the tunneling experiments correspond to the energy of the minima in the electron-ion two-well complex. The gap is defined through the density of states (DOS) inside the electronic bands below the CDW transition. We focus mainly on electronic properties of transition-metal dichalcogenides., Comment: new references added; accepted for publication in Physical Review B. arXiv admin note: substantial text overlap with arXiv:1110.0432

We consider single band of conduction electrons interacting with displacements of the transitional ions.In the classical regime strong coupling transforms the harmonic elastic energy for an ion to the one of the well with two deep minima,so that the system is described in terms of Ising spins. Inter-site interactions via the exchange by electrons order spins at lower temperatures. Extention to the quantum regime is discussed. Below the CDW-transition the energy spectrum of electrons remains metallic because the structural vector Q and the FS sizes are not related.Large values of the CDW gaps seen in the tunneling experiments find their natural explanation as due to the deep energy minima in the bound two-well electron-ion complex., Comment: 6 pages

The essay is an attempt to re-create the wonderful scientific atmosphere that emerged after the basic BCS ideas first arrived in Russia in 1957. It summarizes the most significant contributions to the microscopic theory of superconductivity by Russian physicists during the next few years that have given the theory its modern form., Comment: 20 pages, published in: BCS: 50 YEARS, edited by Leon N Cooper and Dmitri Feldman, World Scientific, 2011

The heterogeneous coexistence of antiferromagnetism (SDW) and superconductivity on a mesoscopic scale was observed in iron-pnictides in many recent experiments. We suggest and discuss the scenario in which the heterogeneity is caused by formation of domain walls inherent to the SDW state of pnictides at a proper doping or under applied pressure. Superconductivity would emerge from the modulated SDW structure. The phenomenon is akin to the FFLO-phase in superconductors., Comment: 5 pages, 1 figure; the title is changed, the estimations of energy cost of one soliton and DOS imbedded into it are added

We discuss the role of striction in the intertwined magnetic and structural phase transitions in the underdoped iron-pnictides. The magneto-elastic coupling to acoustic modes is then derived and estimated in framework of the multiband spectrum for itinerant electrons with nesting features. We argue that the 1-st order character of the magneto-elastic phase transition originates from the lattice instabilities near the onset of spin-density wave order introducing, thus, a shear acoustic mode as a new order parameter. Taking non-harmonic termis in the lattice energy into account may explain the splitting of the structural and magnetic transitions in some oxypnictides. Fluctuations of the magnetic order parameter show up in the precursory temperature dependence of the elastic moduli., Comment: Corrected typo

We argue that charges in underdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ move in a dissipative environment of strong spatial and temporal fluctuations. The unusual temperature dependence of the Hall angle known as "the separation of lifetimes" is reinterpreted and attributed to the appearance of the thermally activated component in the effective number of carriers with the temperature increase. We consider the temperature interval above $T_{c}$ where localization effects can be neglected., Comment: 4 pages, 3 figures

Gradual evolution of two phase coexistence between dynamical and static regimes in cuprates is first investigated in the real space by making use of the available neutron scattering, NMR and mSR data. Analysis of the Hall effect and the ARPES spectra reveals the presence of two groups of charge carriers in LSCO. The T-dependent component is due to the thermal activation of bound electron-hole structures seen near antinodal points in the Brillouin zone, thus introducing the two-component physics also for the momentum representation. Interpretation of so-called "van Hove bands" undergoes drastic changes. Importance of the findings for pseudo-gap physics is stressed. Relation to some recent STM and STS results is discussed., Comment: 8 pages, 6 figures, reported at LEHTSC 2007 conference (Tsukuba), submitted to Journal of Physics: Conference Series

The Hall coefficient data for cuprates show that number of carriers exceeds external doping $x$ at higher $x$ and varies with temperature. Hence, spins on the Cu-sites are not conserved. Activation energy for thermally excited carriers equals the energy between the Fermi surface "arc" and the band bottom near the van Hove singularities. Crossover from marginal Fermi liquid- to pseudogap- regime happens at temperatures at which number of activated carriers gets comparable with the number of externally doped holes. Implications for the $(T,x)$-phase diagram of cuprates are discussed., Comment: 5 pages, 3 figures

We consider competition of Kondo effect and s-wave superconductivity in heavy fermion and mixed valence superconductors, using the phenomenological approach for the periodic Anderson model. Similar to the well known results for single-impurity Kondo effect in superconductors, we have found principal possibility of a re-entrant regime of the superconducting transition temperature, $T_c$, in heavy fermion superconductors in a narrow range of model parameters and concentration of f-electrons. Suppression of $T_c$ in mixed valence superconductors is much weaker. Our theory has most validity in the low-temperature Fermi liquid regime, without re-entrant behavior of $T_c$. To check its applicability, we performed the fit for the $x$-dependence of $T_c$ in Ce$_{1-x}$La$_x$Ru$_3$Si$_2$ and obtained an excellent agreement with the experimental data, although no re-entrance was found in this case. Other experimental data are discussed in the light of our theoretical analysis. In particular, we compare temperatures of the superconducting transition for some known homologs, i.e., the analog periodic lattice compounds with and without f-elements. For a few pairs of homologs superconductivity exists only in the heavy fermion materials, thus confirming uniqueness of superconductivity mechanisms for the latter. We suggest that for some other compounds the value of $T_c$ may remain of the same order in the two homologs, if superconductivity originates mainly on some light Fermi surface, but induces sizable superconducting gap on another Fermi surface,for which hybridization or other heavy fermion effects are more significant., Comment: 11 pages, 4 figures, pdf

We conclude from the analysis of the experimental NMR data for electron-doped cuprates that the Coulomb effects caused by doping lead to dynamical spatial phase separation that contributes to the nuclear spin relaxation. Remarkable, the "infinite-layer" Sr0.9La0.1CuO2 reveals unexpected electron-hole symmetry. Its 63^Cu nuclear spin relaxation rate is the sum of a constant and the temperature dependent dissipation components, moreover, the latter turns out to be identical to the 1/63^T_1(T)-behavior in the stoichiometric hole-type compound YBa2Cu4O8. Connection to fluctuations of a magnetic sub-phase is discussed., Comment: 9 pages, 2 figures, to be published in "Solid State Communications"

We consider 2D surface superconductivity in high magnetic fields parallel to the surface. We demonstrate that the spin-orbit interaction at the surface changes the properties of the inhomogeneous superconducting Larkin-Ovchinnikov-Fulde-Ferrell state that develops above fields given by the paramagnetic criterion. Strong spin-orbit interaction significantly broadens the range of existence of the LOFF phase, which takes the form of periodic superconducting stripes running along the field direction on the surface, leading to the anisotropy of its properties. In connection with experiments by J.H. Schon et al. [Nature 914, 434 (2001)] on superconductivity of electrically doped films of the cuprate material CaCuO2, we also discuss this problem for the d-wave pairing to indicate the possibility of a re-orientation transition as the magnetic field direction is rotated in the plane parallel to the surface. Our results provide a tool for studying surface superconductivity as a function of doping., Comment: 4 pages, 1 fig, revtex 4

Motivated by recent experimental findings, we have developed a theory of the superconducting state for 2D metals without inversion symmetry modeling the geometry of a surface superconducting layer in a field-effect-transistor or near the boundary doped by adsorbed ions. In such systems the two-fold spin degeneracy is lifted by spin-orbit interaction, and singlet and triplet pairings are mixed in the wave function of the Cooper pairs. As a result, spin magnetic susceptibility becomes anisotropic and Knight shift retains finite and rather high value at T=0., Comment: 5 pages, no figures

We consider the effect of isotropic impurity scattering on the exotic superconducting states that arise from the usual BCS mechanism in substances of cubic and hexagonal symmetry where the Fermi surface contains inequivalent but degenerate pockets (e.g. around several points of high symmetry). As examples we look at CeCo$_2$, CeRu$_2$, and LaB$_6$; all of which have such Fermi surface topologies and the former exhibits unconventional superconducting behavior. We find that while these non s-wave states are suppressed by non-magnetic impurities, the suppression is much weaker than would be expected for unconventional superconductors with isotropic non-magnetic impurity scattering., Comment: 4 pages, no figures

We critically investigate the model of a doped excitonic insulator, which recently has been invoked to explain some experimental properties of the ferromagnetic state in Ca_{1-x}La_xB_6. We demonstrate that the ground state of this model is intrinsically unstable towards the appearance of a superstructure. In addition, the model would lead to a phase separation regime and the domain structure which may be prevented by the Coulomb forces only. Recent experiments indicate that a superstructure may indeed show up in this material., Comment: 4 pages, 2 figures, submitted to PRL

We consider the pairing state due to the usual BCS mechanism in substances of cubic and hexagonal symmetry where the Fermi surface forms pockets around several points of high symmetry. We find that the symmetry imposed on the multiple pocket positions could give rise to a multidimensional nontrivial superconducting order parameter. The time reversal symmetry in the pairing state is broken. We suggest several candidate substances where such ordering may appear, and discuss means by which such a phase may be identified., Comment: 5 pages, 2 figures

A phenomenological model with itinerant bands and local states trapped by the lattice on the Cu-sites, is discussed to describe global features of cuprates. Relative energy positions of localized and itinerant states being tuned (thermodynamically or by doping), the system must undergo 1st order Mott metal-insulator transition. Decreasing the local level (from the metallic end of a stoichiometric compound), charge separation instability occurs first before the Mott transition. Crossing and hybridization between local (flat) and itinerant bands introduce a structure in density of states which may account for ``pseudogap'' features in cuprates. Model results in polaronic lattice effects and is rich enough to serve as a phenomenology of cuprates.

We consider singlet magnetism for the uranium ions in UPt$_3$ and URu$_2$Si$_2$ assuming that time-reversal symmetry is broken for the {\em coherent state of intermediate valence}. The relative weight of the two involved configurations should be different for UPt$_3$ and URu$_2$Si$_2$. If in UPt$_3$ the configuration $5f^1$ on the U-ion prevails in the coherent state below the magnetic transition, the magnetic moment would vanish for the particular choice of the {\em ionic} wave function. In case of URu$_2$Si$_2$, the phase transition is non-magnetic in the first approximation -- the magnetic moment arises from a small admixture of a half-integer spin configuration., Comment: 12 pages, RevTex, no figures; Phys. Rev. Lett., to appear