This chapter explores the hydrodynamic models for two-dimensional electronic systems, with a particular emphasis on Dirac fermions. It begins with a kinetic description of charge carriers using the Boltzmann equation, which forms the foundation for deriving the hydrodynamic theory. The chapter discusses the challenges of dealing with long-range Coulomb interactions and introduces the necessary quantum corrections for understanding the behavior of Dirac materials such as graphene. Special attention is given to the fluid-like behavior of charge carriers in 2D materials, facilitated by a fast thermalization process. The chapter introduces key hydrodynamic quantities, including viscosity, momentum relaxation, and collective modes. Through these models, the chapter highlights the critical role of electrostatic interactions, ponderomotive forces, and the collective behavior of charge carriers in bidimensional systems. These fluid descriptions enable the treatment of nonlinear phenomena and the exploration of transient phenomena such as self-sustained growth and solitons. Overall, this chapter provides the theoretical foundation for understanding the hydrodynamic behavior of 2D electron systems and sets the stage for subsequent chapters that explore complex instabilities and wave phenomena.

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Hydrodynamics of Two-Dimensional Electronic Systems

  • Pedro Afonso Cosme e Silva

摘要

This chapter explores the hydrodynamic models for two-dimensional electronic systems, with a particular emphasis on Dirac fermions. It begins with a kinetic description of charge carriers using the Boltzmann equation, which forms the foundation for deriving the hydrodynamic theory. The chapter discusses the challenges of dealing with long-range Coulomb interactions and introduces the necessary quantum corrections for understanding the behavior of Dirac materials such as graphene. Special attention is given to the fluid-like behavior of charge carriers in 2D materials, facilitated by a fast thermalization process. The chapter introduces key hydrodynamic quantities, including viscosity, momentum relaxation, and collective modes. Through these models, the chapter highlights the critical role of electrostatic interactions, ponderomotive forces, and the collective behavior of charge carriers in bidimensional systems. These fluid descriptions enable the treatment of nonlinear phenomena and the exploration of transient phenomena such as self-sustained growth and solitons. Overall, this chapter provides the theoretical foundation for understanding the hydrodynamic behavior of 2D electron systems and sets the stage for subsequent chapters that explore complex instabilities and wave phenomena.