We present an experimental review of the nature of the pseudogap in the cuprate superconductors. Evidence from various experimental techniques points to a common phenomenology. The pseudogap is seen in all high-temperature superconductors and there is general agreement on the temperature and doping range where it exists. It is also becoming clear that the superconducting gap emerges from the normal state pseudogap. The d-wave nature of the order parameter holds for both the superconducting gap and the pseudogap. Although an extensive body of evidence is reviewed, a consensus on the origin of the pseudogap is as lacking as it is for the mechanism underlying high-temperature superconductivity.

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The pseudogap in high-temperature superconductors: an experimental survey

We use time‐, wavelength‐, temperature‐, polarization‐resolved luminescence to elucidate the nature of the absorbing and ‘‘band edge’’ luminescing states in 32 A diameter wurtzite CdSe quantum crystallites. Time‐resolved emission following picosecond size‐selective resonant excitation of the lowest excited state shows two components—a temperature insensitive 100 ps component and a microsecond, temperature sensitive component. The emission spectrum, showing optic phonon vibrational structure, develops a ∼70 wave number red shift as the fast component decays. Photoselection shows the slow component to be reverse polarized at 10 K, indicating this component to be the result of a hole radiationless transition. The 100 ps emitting state is repopulated thermally as temperature increases from 10 to 50 K. All available data are interpreted by postulating strong resonant mixing between a standing wave molecular orbital delocalized inside the crystallite and intrinsic surface Se lone pair states. The apparent excit...

Luminescence properties of CdSe quantum crystallites: Resonance between interior and surface localized states

Intercalation of the layer type transition metal dichalcogenides by a variety of organic molecules, alkali metals, or ‘3d’ transition metals, provides a powerful way to finely tune the electron occupation of the relatively narrow ‘d’ bands met in these solids These transition metal dichalcogenides are highly anisotropic solids, sometimes referred to as ‘two-dimensional’ solids, and the intercalant molecules which are electron donors enter between the layers This can result in profound changes in the electronic properties of the host lattice, and these changes can be understood in terms of charge transfer and increased interlayer separation The phenomena discussed include optical properties, transport properties, super-conductivity, order-disorder phenomena and phase changes, staging, magnetic properties, metal-insulator transitions, Anderson localization, and fast-ion conduction Some possible practical applications are also considered

Electronic properties of intercalation complexes of the transition metal dichalcogenides

The occurrence of charge-density waves in three selected layered transition-metal dichalcogenides-1T-TaS(2), 2H-TaSe(2) and 1T-TiSe(2)-is discussed from an experimentalist's point of view with a particular focus on the implications of recent angle-resolved photoelectron spectroscopy results. The basic models behind charge-density-wave formation in low-dimensional solids are recapitulated, the experimental and theoretical results for the three selected compounds are reviewed, and their band structures and spectral weight distributions in the commensurate charge-density-wave phases are calculated using an empirical tight-binding model. It is explored whether the origin of charge-density waves in the layered transition-metal dichalcogenides can be understood in a unified way on the basis of a few measured and calculated parameters characterizing the interacting electron-lattice system. It is found that the predictions of the standard mean-field model agree only semi-quantitatively with the experimental data and that there is not one generally dominant factor driving charge-density-wave formation in this family of layer compounds. The need for further experimental and theoretical scrutiny is emphasized.

https://iopscience.iop.org/article/10.1088/0953-8984/23/21/213001/pdf

On the origin of charge-density waves in select layered transition-metal dichalcogenides.

This chapter provides an overview of quasiparticle calculations in solids, and, in particular, the GW approximation (GWA). A successful approximation for the determination of excited states of solids is based on the quasiparticle concept and the Green function method. The Coulomb repulsion between electrons leads to a depletion of negative charge around a given electron, and the ensemble of this electron and its surrounding positive screening charge forms a quasiparticle. The mathematical description of quasiparticles is based on the single-particle Green function (G), whose exact determination requires complete knowledge of the quasiparticle self-energy ∑. The self-energy ∑ is a non-Hermitian, energy-dependent, nonlocal operator that describes exchange and correlation effects beyond the Hartree approximation. A determination of the self-energy can only be approximate, and a working scheme for the quantitative calculation of excitation energies in metals, semiconductors, and insulators is the so-called dynamically screened interaction or the GWA. The chapter also discusses (1) the physics and extensions of the GWA; (2) numerical aspects of GWA calculations; (3) applications of the GWA to semiconductors, insulators and metals; and (4) the relevance of GWA calculations to optical response. Finally, the chapter presents parallel algorithms both for reciprocal and real-space/imaginary-time GWA calculations and several alternative methods to determine excited states of solids within density functional theory.

Quasiparticle calculations in solids

We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) on the layered compound 1-T-${\mathrm{TiTe}}_{2}$, whose low-energy properties are those of a normal metal, and analyzed the experimental line shapes in terms of the Fermi-liquid self-energy. We find excellent agreement between the measured and theoretical spectral weight distribution, while line profiles expected for other theoretical models such as the marginal Fermi liquid clearly fail to reproduce the experimental spectra. This demonstrates that ARPES line shapes are able to reflect the nature of an interacting electron system.

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Fermi-liquid line shapes measured by angle-resolved photoemission spectroscopy on 1-T-TiTe2.

We report on the details of the insulator-metal transition (IMT) induced in ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$(${\mathrm{Ca}}_{\mathit{z}}$,${\mathit{R}}_{1\mathrm{\ensuremath{-}}\mathit{z}}$)${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8+\mathit{y}}$ (R=Y, Gd, Nd) by ${\mathrm{Ca}}^{2+}$ doping. The resistivity in the insulating regime is analyzed using a generalized hopping approach based on the connectivity criterion. This enables us to estimate the dependence of the localization radius ${\mathit{a}}_{\mathit{H}}$ on the Ca concentration independent of dimensionality. Insulating samples with a Y content not too far from the critical concentration ${\mathit{z}}_{\mathit{C}}$=(0.43\ifmmode\pm\else\textpm\fi{}0.02) show metallic conduction at high temperature and hopping conduction at low temperature. This shows the coexistence of delocalized and localized states separated by a disorder-induced mobility edge. Ultraviolet-photoemission-spectroscopy (UPS) spectra give evidence for both a shift in the Fermi level to lower energies and the development of new states at the Fermi level. The existence of a mobility edge together with the shift in ${\mathit{E}}_{\mathit{F}}$ upon ${\mathrm{Ca}}^{2+}$ doping shows that the transition is probably of the Anderson type. We present a schematic picture for the density of states in the vicinity of ${\mathit{E}}_{\mathit{F}}$ based on the results of spectroscopic and transport data. For this density of states we calculate the electrical resistivity using the Kubo-Greenwood formula. The results are in good qualitative agreement with the experiments. At the IMT the localization radius diverges and the metallic conductivity vanishes following a scaling law \ensuremath{\sigma}=${\mathrm{\ensuremath{\sigma}}}_{0}${1-z/${\mathit{z}}_{\mathit{C}}$${\mathrm{}}}^{\mathrm{\ensuremath{\eta}}}$, with a critical exponent \ensuremath{\eta}=1A.

Scaling behavior at the insulator-metal transition in Bi2Sr2(CazR1-z)Cu2O8+y where R is a rare-earth element.

The electronic structure of high-Tc Bi2Sr2CaCu2O8 single crystals in the vicinity of the Fermi level EF is determined down to about 0.7Tc by high-resolution angle-resolved photoemission spectroscopy applying HeI and synchrotron radiation. Spectra taken with 18 eV photon energy at an emission angle of 9° reveal a clear Fermi edge T > Tc. For T < Tc the emission intensity changes distinctly—at EF it decreases whereas it increases at about 100 meV below EF—accompanied by a clear shift of the emission onset to higher binding energy. These observations can be consistently explained by the opening of an energy gap of about 30 meV in the superconducting quasi-particle density of states, yielding a ratio Δ (0)/kB Tc about twice as large as the BCS value indicating that Bi2Sr2CaCu2O8 is a strong-coupling superconductor.

On the Superconducting Energy Gap in Bi2Sr2CaCu2O8 Investigated by High-Resolution Angle-Resolved Photoemission

Determination des bandes interdites de surface entre l'etat rempli de liaison pendante de l'anion (A 5 ) et de l'etat vide du cation (C 3 ). On se place aux points Γ, X', X et M de la zone de Brillouin de surface. Comparaison des resultats avec les excitations optiques de surface et les donnees de perte d'energie electronique

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Direct determination of III-V semiconductor surface band gaps

Low-energy-electron-diffraction (LEED) and angle-resolved inverse photoemission spectroscopy (ARIPES) have been applied to the cleaved surface of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ single crystals. The LEED pattern shows a surface lattice which is identical to the superlattice found in the bulk structure. ARIPES along the \ensuremath{\Gamma}X(${a}^{\mathrm{*}}$) direction yields nondispersive unoccupied electronic states at 2.9 and \ensuremath{\sim}5 eV above the Fermi energy attributed to Bi-O derived conduction bands. At 0.47 \ensuremath{\Gamma}X the experimental density of states at the Fermi level increases. This may be due to the crossing of the O(1) band through ${E}_{F}$ derived from oxygen atoms in the Cu-O planes.

R. Manzke

Papers

Fermi-liquid line shapes measured by angle-resolved photoemission spectroscopy on 1-T-TiTe2.

Scaling behavior at the insulator-metal transition in Bi2Sr2(CazR1-z)Cu2O8+y where R is a rare-earth element.

On the Superconducting Energy Gap in Bi2Sr2CaCu2O8 Investigated by High-Resolution Angle-Resolved Photoemission

Direct determination of III-V semiconductor surface band gaps

Surface study of the 83-K superconductor Bi 2 Sr 2 CaCu 2 O 8 by low-energy electron diffraction and angle-resolved inverse photoemission spectroscopy