Search Results

This chapter places the work presented in the previous chapters on the electron momentum density and band structure in condensed matter in the context of other probes. Specifically, studies by techniques such as positron annihilation, which is traditionally used to reconstruct Fermi surface topology and angle-resolved photo-emission (ARPES) used to reconstruct k-space density of states. Electron scattering coincidence spectroscopy, which reveals the three-dimensional momentum density in gaseous molecules for each shell of electrons, is then compared to Compton coincidence spectroscopy. The insight that is afforded by spin dependent x-ray Compton scattering is compared to resonant x-ray diffraction studies of magnetization. The chapter finishes with a comparison between x-ray Compton scattering studies of electron density distributions and Deep Inelastic Neutron Scattering (DINS) studies of nuclear momentum distributions.

Gap imaging STS using a lattice-tracking variable-temperature scanning tunnelling microscope is applied to HTC cuprate superconductor Bi2212. The results indicate an anti-correlation between local gap and local zero-bias density of states. No correlation is found between gap and strength of the boson-like dip feature. This chapter concludes that the driving force for the pairing is of electronic origin. An internal proximity effect between neighbouring regions is found in the observed growth of superconductivity with temperature. The localized state induced by a Zn impurity is displayed and theoretically explicated. The superlattice modulation in Bi2212 is described, as is the charge ordering within flux-line cores. The relation between STS and angle resolved photoemission spectroscopy ARPES is explained. Features of colossal magnetoresistive CMR ferromagnetic manganites are explicated with STS.

After brief review of important electrical transport measurements, optical and Raman methods, techniques of angle-resolved photoemission spectroscopy (ARPES) and scanning tunnelling microscopy, spectroscopy (STM/STS) and scanning tunneling potentiometry are introduced. It is pointed out that ARPES, like conventional transport measurements, average over a large area, while STM and scanning single electron transistor (SSET) measurements are local, on an atomic scale in some cases. Capacitance spectroscopy is described and the scanning single electron transistor is described as a method of mapping surface potential and determining a density-of-states quantity called the inverse compressibility. The use of the latter SSET method in finding fractional quantum Hall effects is described.

This chapter discusses various methods that have been used to measure the energy spectrum of electrons in both metals and insulators. For metals a property of paramount importance is the detailed shape of the Fermi surface and the accompanying Fermi velocity, since together they affect transport and other phenomena. Methods to measure these quantities include various magneto-acoustic effects (e.g., the geometric resonance phenomenon), the Gantmakher and Sondheimer size effects, the Azbel–Kaner cyclotron resonance, the anomalous skin effect, the high-field magneto-resistance (as it relates to open versus closed orbits), and various quantum oscillations, the most important of which is the de Hass–van Alphen effect. For determining the energy spectrum at energies below the Fermi surface, the most powerful technique is angle resolved photo-emission spectroscopy (ARPES) which, with the emergence of synchrotron sources, has become increasingly important. Also of growing importance is inverse photo-emission spectroscopy (IPS), a special case of which is termed bremsstrahlung isochromat spectroscopy (BIS). Here the roles of the incoming photon and the final state electron are reversed: electrons of known energy (and angle) impinge on the surface and (in the BIS variant) the energy spectrum of the emitted photons is measured. This technique probes the spectrum for energies above the Fermi energy.

Electron energy bands in solids are introduced. Free electron theory for metals is presented: the Fermi gas, Fermi energy and temperature. Electrical and thermal conductivity are interpreted, including the Wiedermann–Franz law. The Hall effect and information it brings about charge carriers is discussed. Plasma oscillations of conduction electrons and the optical properties of metals are examined. Formation of quasi-particles of an electron and its screening cloud are discussed. Electron-electron and electron-phonon scattering and how they affect the mean free path are treated. Then the analysis of crystalline materials using electron Bloch waves is presented. Tight and weak binding cases are examined. Electron band structure is explained including Brillouin zones, electron kinematics and effective mass. Fermi surfaces in crystals are treated. The ARPES technique for exploring dispersion relations is explained.