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Interaction effects in quantum-confined systems give rise to the Coulomb blockade phenomenon in electronic transport. This chapter discusses the Coulomb blockade phenomenon in quantum dots. As a first stage, the phenomenon is explained on a qualitative level. The second part of the chapter discusses the quantum states of a dot isolated from the leads within different approximative schemes, such as the capacitance model complemented with single-particle spectra, Hartree– and Hartree–Fock approximations, and the constant interaction model. The physics of quantum dot helium is discussed in detail as a paradigmatic interacting model system with spin. In the third part of the chapter, transport through quantum dots is discussed in the resonant tunnelling and the sequential tunnelling pictures. The chapter ends with a discussion of cotunneling processes and the Kondo effect.

This chapter presents simple ideas for understanding how spin-polarized currents can be used to exert spin-transfer torques in magnetic devices. The chapter reviews recent progress for measuring the magnetic dynamics that result from spin-transfer torques in 100-nm-scale metallic spin valves and magnetic tunnel junctions. The chapter also discusses how the transport of spin and charge in magnetic devices changes when the structures are made even smaller, extending from magnetic particles a micron in diameter, to a few nanometers, and down to a single molecule. As the size of the magnet shrinks, effects such as Coulomb blockade and energy-level quantization can become dominant, and it becomes necessary to move beyond simple independent-electron models to consider the true correlated many-electron quantum states at the root of ferromagnetism.

This chapter discusses the phenomenon of Coulomb blockade, which takes place in small junctions. It first explains conditions of observing Coulomb blockade in single- or multiple junction systems and then details the orthodox theory of single-electron tunnelling, which consists of calculating the tunnelling rates and using them in a master equation for the charge states. This theory allows understanding of the properties of a single-electron transistor. The higher-order cotunneling is explained briefly. The phenomenon of dynamical Coulomb blockade arising in single junctions placed in high-resistance environments is discussed in detail. The chapter closes by describing main single-electron devices besides the conventional single-electron transistor: Coulomb blockade thermometer, radio frequency single-electron transistor, and a single electron pump.

Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.

This chapter demonstrates approaches to the treatment of macroscopically inhomogeneous materials. The conception and criteria of granularity are introduced and experimental examples of metal-insulator transition are presented. The nature of the transition is tightly connected to the phenomenon of Coulomb blockade: electron tunneling between the grains is blocked because charging of small grains requires Coulomb energy larger than the temperature. The concept of a granular material is not restricted to cermets — a mixture of metallic and insulating grains of different sizes but quasi-spherical in shape. It can be extended to materials with fractal grains where the insulating volume resembles a loose glomus of thin insulating sheets.

This chapter reviews several types of nonlinear behaviour in nanotubes and graphene resonators. It first discusses a scenario where damping is described by a nonlinear force. Several experimental facts support this: the quality factor varies with the motional amplitude as a power law whose exponent coincides with the value predicted by the nonlinear damping model, hysteretic behaviour (of the motional amplitude vs. driving frequency) is absent in some resonators even for large driving forces, as expected when nonlinear damping forces are large, and the linear damping force extracted from parametric excitation measurements is significantly smaller than the nonlinear damping force. The chapter then reviews parametric excitation measurements, an alternative actuation method based on nonlinear dynamics. Finally, it discusses experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling is so strong that the associated force acting on the nanotube is highly nonlinear with displacement and velocity.

Quantum dots are small islands connected to typically metallic electrodes. Their small size shows up in the large spacing of the single-electron energy levels inside these islands. This chapter explains the main transport phenomena taking place in quantum dots, and different theoretical approaches constructed to describe them. The approaches include the self-consistent mean field theory relevant in the weakly interacting limit and the theory of Coulomb blockade in the strongly interacting limit. Between these limits one can find the Kondo effect, which is phenomenologically explained in the chapter. The discussion also covers the properties of double quantum dots, and some of their properties, such as the spin states, Pauli spin blockade, and usage as quantum bits.

This chapter discusses the formal framework and applications of time-dependent density-functional theory (TDDFT) to nanoscale transport. It begins with a brief overview of the basic concepts of nanoscale transport, such as transmission coefficients, conductance, and the Landauer approach. An exact expression for the conductance is derived under the assumption of weak bias. The starting point is the linear current response equation. An exchange-correlation contribution to the resistivity is obtained, even if the transport is in the steady-state, zero-frequency regime. This contribution is shown to become significant for narrow junctions. Next, the finite-bias case is discussed. A TDDFT approach for time-dependent transport is formulated in which a finite scattering region is coupled to infinite leads. The steady-state transmission coefficient is expressed in terms of nonequilibrium Green's functions. The Coulomb blockade regime of transport is discussed. Lastly, the master equation approach and stochastic TDDFT for open systems are reviewed.