Aspects of Linear and Nonlinear Transport in Mesoscopic Systems

Abstract

We begin this thesis with a general introduction to mesoscopic physics and the scattering approach to transport. The subsequent chapters are broken up into two related topics in mesoscopic physics. The first of these topics, in Chapters 2 and 3, focuses on developing a scattering approach to treat weakly nonlinear transport of charge and heat through mesoscopic systems. In Chapter 2 we develop a weakly nonlinear theory for thermoelectric transport in purely metallic systems while emphasizing its importance in the study of thermoelectric efficiencies. In Chapter 3 we extend the theory to treat electric current rectification in metallic systems contacted to superconducting islands. The next topic we discuss is on how electric current noise can be used to make measurements in mesoscopic systems. In Chapter 4 we demonstrate that electric current noise in a temperature probe can provide a measure of an "effective" local temperature in a non-equilibrium system. We show that this electrical measurement is consistent with a thermal measurement of the temperature probe, within the limit of the validity of a Sommerfeld expansion. Finally, in Chapter 5 we describe how current noise can be used to measure spin accumulation in reservoirs connected to a scatterer with strong spin-orbit coupling. Throughout this thesis we emphasize conservation relations and provide general multi-terminal expressions whenever possible.