Fermi Surfaces, Fermi Liquids, and High-Temperature Superconductors

Why have band theorists been so successful in explaining and predicting novel superconductors?

In this contribution to the J. Phys.: Condens. Matter memorial issue in honor of Sandro Massidda I reflect on a phenomenon Sandro had been a part of. While theoretical condensed matter physicists have made, over the years, exciting and most elegant contributions to the theory of superconductivity (which, in and by itself, is one of the most beautiful constructs in theoretical physics), some of them of utmost importance, they have had less success in predicting and explaining superconducting states and mechanisms in specific materials. More down-to-earth computational materials scientists, who often go by the moniker 'band theorists', have been much more successful in applying (usually other people's) ideas in such circumstances. In this essay I give some examples, largely drawn from my own experience, and speculate on their meaning.

d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry

A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the two-dimensional geometry of the Fermi surface (FS). Phase diagrams on the σ0 − α plane—here, σ0 is the ratio between the energy gaps in the parent pure CDW and superconducting states, and the quantity 2α is connected with the degree of dielectric (CDW) FS gapping—were obtained for various possible configurations of the order parameters in the momentum space. Relevant tunnel and photoemission experimental data for high-Tc oxides are compared with theoretical predictions. A brief review of the results obtained earlier for the coexistence between s-wave superconductivity and CDWs is also given.

The phase diagram for coexisting d-wave superconductivity and charge-density waves: cuprates and beyond

Phase diagrams of d-wave superconductivity characterized by an order parameter Δ coexisting with charge-density waves (CDWs) characterized by an order parameter Σ were constructed for the two-dimensional Fermi surface (FS) appropriate to, e.g., cuprates. CDWs were considered as an origin of the pseudogap appearing at antinodal FS sections of the d(x2-y2) superconductor. Two types of the Σ-reentrance were found: with the temperature, T, and with the opening of the CDW sector, 2α. The angular plots in the momentum space for the resulting gap profile over the FS ('gap roses') were obtained. The gap patterns are rather involved, giving insight into the difficulties of the interpretation of photoemission spectra. It was shown that the Σ-Δ coexistence region exists even for the complete dielectric gapping due to the distinction between the superconducting and CDW order parameter symmetries. The checkerboard and unidirectional CDW configurations were examined, and both the phase diagrams and the behavior with T and α of the order parameters were found to differ. A more general case with a non-zero mismatch angle β between the superconducting lobes and the CDW sectors was analyzed, the case β = π/4 corresponding to the d(xy) symmetry of the superconducting order parameter. The phase diagrams were found to be sensitive to β-variations, showing that internal strains and external pressure can drastically affect the behavior of Σ(T) and Δ(T).

Density functional study of LaFeAsO(1-x)F(x): a low carrier density superconductor near itinerant magnetism

Density functional studies of 26 K superconducting LaFeAs(O,F) are reported. We find a low carrier density, high density of states, N(E(F)), and modest phonon frequencies relative to T(c). The high N(E(F)) leads to proximity to itinerant magnetism, with competing ferromagnetic and antiferromagnetic fluctuations and the balance between these controlled by the doping level. Thus LaFeAs(O,F) is in a unique class of high T(c) superconductors: high N(E(F)) ionic metals near magnetism.

Photoemission Studies of High- T c Superconductors: The Superconducting Gap

Over the last several years there have been great improvements in the energy resolution and detection efficiency of angle-resolved photoemission spectroscopy. These improvements have made it possible to discover a number of fascinating features in the electronic structure of the high transition temperature (T(c)) superconductors: apparently bandlike Fermi surfaces, flat-band saddle points, and nested Fermi surface sections. Recent work suggests that these features, previously thought explainable only by one-electron band theory, may be better understood with a many-body approach. Furthermore, other properties of the high-T(c) superconductors, which are difficult to understand with band theory, are well described using a many-body picture. Angle-resolved photoemission spectroscopy has also been used to investigate the nature of the superconducting pairing state, revealing an anisotropic gap consistent with a d-wave order parameter and fueling the current debate over s-wave versus d-wave superconductivity.