Search Results

This chapter continues the discussion of interaction effects in transport starts from the fractional quantum Hall effect in Chapter 16, but returns to the case of zero magnetic field. The influence of screening on the Drude conductivity and its temperature dependence are elucidated. Interaction-related quantum corrections to the Drude conductivity are discussed in the picture of multiple scattering at Friedel oscillations.

This chapter uses a case study of two-dimensional electron gases in heterostructures to illustrate the theoretical concepts put forward in Chapters 7 and 8. The electrostatics and the field effect in these structures are worked out, and the capacitance between the electron gas and a top-gate is determined. Quantum mechanics is introduced in the approximation of the Fang–Howard variational approach. The theory of linear screening in two-dimensional electron gases is discussed in detail, including the Thomas–Fermi approximation, and the appearance of Friedel oscillations in the electron density. Spin-orbit interaction effects in two-dimensional electron gases are discussed, and finally, the characteristic quantities of two-dimensional electron gases are summarized.

Chapter 10 reviews both homogeneous and inhomogeneous quantum plasma dielectric response phenomenology starting with the RPA polarizability ring diagram in terms of thermal Green’s functions, also energy eigenfunctions. The homogeneous dynamic, non-local inverse dielectric screening functions (K) are exhibited for 3D, 2D, and 1D, encompassing the non-local plasmon spectra and static shielding (e.g. Friedel oscillations and Debye-Thomas-Fermi shielding). The role of a quantizing magnetic field in K is reviewed. Analytically simpler models are described: the semiclassical and classical limits and the hydrodynamic model, including surface plasmons. Exchange and correlation energies are discussed. The van der Waals interaction of two neutral polarizable systems (e.g. physisorption) is described by their individual two-particle Green’s functions: It devolves upon the role of the dynamic, non-local plasma image potential due to screening. The inverse dielectric screening function K also plays a central role in energy loss spectroscopy. Chapter 10 introduces electromagnetic dyadic Green’s functions and the inverse dielectric tensor; also the RPA dynamic, non-local conductivity tensor with application to a planar quantum well. Kramers–Krönig relations are discussed. Determination of electromagnetic response of a compound nanostructure system having several nanostructured parts is discussed, with applications to a quantum well in bulk plasma and also to a superlattice, resulting in coupled plasmon spectra and polaritons.