Lev P. Gor’kov

CONVENTIONAL MECHANISMS FOR EXOTIC SUPERCONDUCTIVITY

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.

Pressure and high-Tc superconductivity in sulfur hydrides.

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.

Role of striction at magnetic and structural transitions in iron pnictides

We discuss the role of striction in the intertwined magnetic and structural phase transitions in the underdoped iron pnictides. The magnetoelastic 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 first-order character of the magnetoelastic phase transition originates from the lattice instabilities near the onset of spin-density wave order introducing, thus, a shear acoustic mode as another order parameter. Taking nonharmonic terms 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.

Phonon mechanism in the most dilute superconductor n-type SrTiO3

Significance Low-temperature superconductivity of SrTiO3 gives insight into high-TC (up to 110 K) superconductivity in atomic-thin FeSe layers on SrTiO3. In low-doped SrTiO3 long-range electron interactions with longitudinal (LO) polar modes provide the unique pairing mechanism. Frequencies of polar modes larger than the Fermi energy imply nonadiabatic pairing rather than the usual separate treatment of electron and phonon degrees of freedom. Transport experiments reveal the mobility edge. Random localized states control the interaction between electrons and LO phonons via the magnitude of the dielectric constant. TC is proportional to the Fermi energy. Interaction of the FeSe electrons with surface LO phonons is governed by the dielectric constant at a diffuse surface. Larger 2D Fermi surface results in higher TC for FeSe/SrTiO3. Superconductivity of n-doped SrTiO3, which remained enigmatic for half a century, is treated as a particular case of nonadiabatic phonon pairing. Motivated by experiment, we suggest the existence of the mobility edge at some dopant concentration. The itinerant part of the spectrum consists of three conduction bands filling by electrons successively. Each subband contributes to the superconducting instability and exhibits a gap in its energy spectrum at low temperatures. We argue that superconductivity of n-doped SrTiO3 results from the interaction of electrons with several longitudinal (LO) optical phonons with frequencies much larger than the Fermi energy. Immobile charges under the mobility edge threshold increase the “optical” dielectric constant far above that in clean SrTiO3 placing control on the electron–LO phonon interaction. TC initially grows as density of states at the Fermi surface increases with doping, but the accumulating charges reduce the electrons–polar-phonon interaction by screening the longitudinal electric fields. The theory predicts maxima in the TC-concentration dependence indeed observed experimentally. Having reached a maximum in the third band, the transition temperature finally decreases, rounding out the TC (n) dome, the three maxima with accompanying superconducting gaps emerging consecutively as electrons fill successive bands. This arises from attributes of the LO optical phonon pairing of electrons. The mechanism of LO phonons opens the path to increasing superconducting transition temperature in bulk transition-metal oxides and other polar crystals, and in charged 2D layers at the LaAaO3/SrTiO3 interfaces and on the SrTiO3 substrates.

Colloquium : High pressure and road to room temperature superconductivity

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.

Back to Mechanisms of Superconductivity in Low-Doped Strontium Titanate

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.

Notes on Microscopic Theory of Superconductivity

Abstract The first part of this chapter traces several of the most dramatic events in the long history of studying the superconductivity phenomenon. The second part discusses, in somewhat more detail, the evolution of the theoretical ideas that finally lead to the microscopic theory in its modern form.

Foundations of Superconductivity and Extension to Less-Common Systems

The review of fundamentals of the microscopic theory of superconductivity, as a whole, serves to the purpose to elicit a knowledge about theoretical results and qualitative statements which would be robust enough to allow a judgment regarding the nature of superconductivity in such uncommon superconductors, as cuprates or superconductors of the Heavy Fermion family.

NON-FERMI LIQUID BEHAVIOR OF KINETIC CHARACTERISTICS IN QUASI-ONE-DIMENSIONAL ORGANIC CONDUCTORS

Years ago W. Little has suggested a mechanism1 by which, he hoped, it may be possible to dramaticaly increase the transition temperatures for superconductivity in the new generation of materials based on linear organic components. This publication stimulated enourmous experimental activity in syntheses and study of the absolutely new class of conducting materials-the organic conductors. Now, as the result of collective international efforts, we have the fascinating new world of organic compounds, and some of them are superconductors with a remarkably high (~10K) transition temperature. Recall that the vast majority of these new metals do not even contain any metallic element at all!

On possible observation of nontrivial magnetic order parameter by neutrons (abstract)

We consider neutron scattering in a system with spin nematic or triple spin correlator order parameter. External magnetic field induces different magnetizations on different sublattices in this system. As a result, one can observe purely magnetic Bragg peaks for polarized neutron scattering in an applied external magnetic field. We present estimates of intensities in the Bragg peaks and their dependence on the external magnetic field. This could be a possible test for nontrivial magnetic order in the heavy fermion compounds URu2Si2 and UPt3.1