# Extended systems

# Extended systems

This chapter deals with the electron dynamics in extended systems; more precisely, three-dimensional periodic solids. It begins with a brief review of electronic band-structure theory, explaining the difference between metals and insulators. It then considers linear-response theory in periodic systems, with particular emphasis on the dielectric tensor. The macroscopic dielectric function is the quantity one is usually interested in. The next section discusses the spectroscopic properties of charge-density fluctuations in metallic systems. Plasmons are introduced for homogeneous systems and real metals. Time-dependent density-functional theory gives very accurate results for plasmon dispersions. The third section focuses on optical absorption and excitons in semiconductors and insulators. It begins with a simple introduction of excitons, and then shows that time-dependent density-functional theory requires long-ranged exchange-correlation kernels to produce excitonic binding. A simple two-band model is discussed in some detail. Finally, time-dependent current-density-functional theory for periodic systems is reviewed.

*Keywords:*
periodic systems, band structure, dielectric tensor, macroscopic dielectric function, plasmons, excitons, plasmon dispersions, time-dependent current-density-functional theory

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