The surprising discovery of high-temperature superconductivity in a material containing a strong magnet—iron—has led to thousands of publications. By placing all the data in context, it becomes clear what we know and where we are headed.

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High-temperature superconductivity in iron-based materials

The recently discovered Fe-pnictide and chalcogenide superconductors display low-temperature properties suggesting superconducting gap structures which appear to vary substantially from family to family, and even within families as a function of doping or pressure. We propose that this apparent nonuniversality can actually be understood by considering the predictions of spin fluctuation theory and accounting for the peculiar electronic structure of these systems, coupled with the likely 'sign-changing s-wave' (s?) symmetry. We review theoretical aspects, materials properties and experimental evidence relevant to this suggestion, and discuss which further measurements would be useful to settle these issues.Satisfactoriness has to be measured by a multitude of standards, of which some, for aught we know, may fail in any given case; and what is more satisfactory than any alternative in sight, may to the end be a sum of pluses and minuses, concerning which we can only trust that by ulterior corrections and improvements a maximum of the one and a minimum of the other may some day be approached.??????????????????????William James, Meaning of Truth

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Gap symmetry and structure of Fe-based superconductors

A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials'' In order to establish this class of materials, we illustrate how Dirac fermions emerge in multiple entirely different condensed matter systems and we discuss how Dirac fermions have been identified experimentally using electron spectroscopy techniques (angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy) As a consequence of their common low-energy excitations, this diverse set of materials shares a significant number of universal properties in the low-energy (infrared) limit We review these common properties including nodal points in the excitation spectrum, density of states, specific heat, transport, thermodynamic properties, impurity resonances, and magnetic field responses, as well as discuss many-body interaction effects We further review how the emergence of Dirac excitations is controlled by specific symmetries of the material, such as time-reversal, gauge, and spin-orbit symmetries, and how by breaking these symmetries a finite Dirac mass is generated We give examples of how the interaction of Dirac fermions with their distinct real material background leads to rich novel physics with common fingerprints such as the suppression of back scattering and impurity-induced resonant states

Dirac materials

The recently discovered Fe-pnictide and chalcogenide superconductors display low-temperature properties suggesting superconducting gap structures which appear to vary substantially from family to family, and even within families as a function of doping or pressure. We propose that this apparent nonuniversality can actually be understood by considering the predictions of spin fluctuation theory and accounting for the peculiar electronic structure of these systems, coupled with the likely 'sign-changing s-wave' (s\pm) symmetry. We review theoretical aspects, materials properties and experimental evidence relevant to this suggestion, and discuss which further measurements would be useful to settle these issues.

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O(8+x). Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.

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Ubiquitous Interplay between Charge Ordering and High-Temperature Superconductivity in Cuprates

High-transition-temperature (high-Tc) superconductivity is ubiquitous in the cuprates containing CuO2 planes, but each cuprate has its own character. The study of the material dependence of the d-wave superconducting gap (SG) should provide important insights into the mechanism of high-Tc superconductivity. However, because of the ‘pseudogap’ phenomenon, it is often unclear whether the energy gaps observed by spectroscopic techniques really represent the SG. Here, we use scanning tunnelling spectroscopy to image nearly optimally doped Ca2−xNaxCuO2Cl2(Na-CCOC) with Tc=25–28 K. It enables us to observe the quasiparticle interference effect in this material, through which we obtain unambiguous information on the SG. Our analysis of quasiparticle interference in Na-CCOC reveals that the SG dispersion near the gap node is almost identical to that of Bi2Sr2CaCu2Oy (Bi2212) at the same doping level, despite the Tc of Bi2212 being three times higher than that of Na-CCOC. We also find that the SG in Na-CCOC is confined in narrower energy and momentum ranges than Bi2212, which explains—at least in part—the remarkable material dependence of Tc.

Quasiparticle interference and superconducting gap in Ca 2− x Na x CuO 2 Cl 2

When electrons pair in a superconductor, quasi-particles develop an acute sensitivity to different types of scattering potential that is described by the appearance of coherence factors in the scattering amplitudes. Although the effects of coherence factors are well established in isotropic superconductors, they are much harder to detect in their anisotropic counterparts, such as high-superconducting-transition-temperature cuprates. We demonstrate an approach that highlights the momentum-dependent coherence factors in Ca2– x Na x CuO2Cl2. We used Fourier-transform scanning tunneling spectroscopy to reveal a magnetic-field dependence in quasi-particle scattering interference patterns that is sensitive to the sign of the anisotropic gap. This result is associated with the d -wave coherence factors and quasi-particle scattering off vortices. Our technique thus provides insights into the nature of electron pairing as well as quasi-particle scattering processes in unconventional superconductors.

Coherence Factors in a High-Tc Cuprate Probed by Quasi-Particle Scattering Off Vortices

We performed high-resolution scanning tunneling microscopy/spectroscopy on an optimally-doped Ca2−xNaxCuO2Cl2 crystal with Tc ∼ 25 K. The so-called “checkerboard” local-density-of-state modulation previously found in heavily underdoped regime also manifests in the spectroscopic map of the optimally-doped sample. In addition, spatially-inhomogeneous energy gap with peaks at the gap edges is observed below about 10 meV. The gap tends to be buried at elevated temperatures and correlates with the checkerboard modulation. These results suggest that the gap is related to superconductivity which coexists with the checkerboard modulation.

K. Ohishi

Papers

Quasiparticle interference and superconducting gap in Ca 2− x Na x CuO 2 Cl 2

Coherence Factors in a High-Tc Cuprate Probed by Quasi-Particle Scattering Off Vortices

Low-energy spectroscopic mapping studies in optimally-doped Ca2−xNaxCuO2Cl2