Phonon mechanism in the most dilute superconductor: n-type SrTiO3

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 figure

Exotic ground states and impurities in multiband superconductors

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 figure

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.Comment: 67 pages,7 figure

Developing BCS ideas in the former Soviet Union

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, 201