The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for 1 the rotation of an electron spin into a superposition of up and down, 2 the measurement of the quantum state of an individual spin, and 3 the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins i.e., single spintronics.

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Spins in few-electron quantum dots

Using molecules as electronic components is a powerful new direction in the science and technology of nanometre-scale systems1. Experiments to date have examined a multitude of molecules conducting in parallel2,3, or, in some cases, transport through single molecules. The latter includes molecules probed in a two-terminal geometry using mechanically controlled break junctions4,5 or scanning probes6,7 as well as three-terminal single-molecule transistors made from carbon nanotubes8, C60 molecules9, and conjugated molecules diluted in a less-conducting molecular layer10. The ultimate limit would be a device where electrons hop on to, and off from, a single atom between two contacts. Here we describe transistors incorporating a transition-metal complex designed so that electron transport occurs through well-defined charge states of a single atom. We examine two related molecules containing a Co ion bonded to polypyridyl ligands, attached to insulating tethers of different lengths. Changing the length of the insulating tether alters the coupling of the ion to the electrodes, enabling the fabrication of devices that exhibit either single-electron phenomena, such as Coulomb blockade, or the Kondo effect.

Coulomb blockade and the Kondo effect in single-atom transistors

The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and "exact" diagonalization methods. The spontaneous magnetization due to Hund's rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and the regime of strong magnetic fields in finite dot is examined. In addition, quasi-one-dimensional rings, deformed dots, and dot molecules are considered. (Less)

/pdf/electronic-structure-of-quantum-dots-c4uhdr9l0b.pdf

Electronic structure of quantum dots

I. Introduction (Preface, Nanostructures in Si Inversion Layers, Nanostructures in GaAs-AlGaAs Heterostructures, Basic Properties). 
II. Diffusive and Quasi-Ballistic Transport (Classical Size Effects, Weak Localization, Conductance Fluctuations, Aharonov-Bohm Effect, Electron-Electron Interactions, Quantum Size Effects, Periodic Potential). 
III. Ballistic Transport (Conduction as a Transmission Problem, Quantum Point Contacts, Coherent Electron Focusing, Collimation, Junction Scattering, Tunneling). 
IV. Adiabatic Transport (Edge Channels and the Quantum Hall Effect, Selective Population and Detection of Edge Channels, Fractional Quantum Hall Effect, Aharonov-Bohm Effect in Strong Magnetic Fields, Magnetically Induced Band Structure).

/pdf/quantum-transport-in-semiconductor-nanostructures-1n3dkljf6x.pdf

Quantum Transport in Semiconductor Nanostructures

Manipulating a stubborn magnet Spintronics is an alternative to conventional electronics, based on using the electron's spin rather than its charge. Spintronic devices, such as magnetic memory, have traditionally used ferromagnetic materials to encode the 1's and 0's of the binary code. A weakness of this approach—that strong magnetic fields can erase the encoded information—could be avoided by using antiferromagnets instead of ferromagnets. But manipulating the magnetic ordering of antiferromagnets is tricky. Now, Wadley et al. have found a way (see the Perspective by Marrows). Running currents along specific directions in the thin films of the antiferromagnetic compound CuMnAs reoriented the magnetic domains in the material. Science, this issue p. 587; see also p. 558 Transport and optical measurements are used to demonstrate the switching of domains in the antiferromagnetic compound CuMnAs. [Also see Perspective by Marrows] Antiferromagnets are hard to control by external magnetic fields because of the alternating directions of magnetic moments on individual atoms and the resulting zero net magnetization. However, relativistic quantum mechanics allows for generating current-induced internal fields whose sign alternates with the periodicity of the antiferromagnetic lattice. Using these fields, which couple strongly to the antiferromagnetic order, we demonstrate room-temperature electrical switching between stable configurations in antiferromagnetic CuMnAs thin-film devices by applied current with magnitudes of order 106 ampere per square centimeter. Electrical writing is combined in our solid-state memory with electrical readout and the stored magnetic state is insensitive to and produces no external magnetic field perturbations, which illustrates the unique merits of antiferromagnets for spintronics.

/pdf/electrical-switching-of-an-antiferromagnet-2bcb2cox7l.pdf

Electrical switching of an antiferromagnet

An envelope-function formalism analogous to the effective-mass theory for electrons is developed to treat long-wavelength phonons in semiconductor heterostructures. It consists of a set of differential equations for phonon envelope functions and their boundary conditions at interfaces. For acoustic phonons the present theory becomes equivalent to the elasticity theory. For optical phonons there are two cases to which our formalism is applicable. In the first case, in which the bulk optical bands of constituent materials overlap considerably, as in InAs/GaSb and GaAs/Ge, the boundary conditions are written in the form of linear relations among envelopes and their derivatives on both sides of the interface. The boundary conditions strongly depend not only on the materials but also on the atomic configuration at interfaces. In the second case, where there is a large gap between the bulk optical branches, as in GaAs/AlAs, the boundary conditions that the envelopes should vanish at interfaces are generally appropriate.

Envelope-function formalism for phonons in heterostructures.

Phonons in GaAs/AlAs superlattices.

Calculations of the Hall resistance of quasi-one-dimensional electron systems on a GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterointerface are performed. It is shown in a weak-link model of Hall probes that the Hall resistance strongly depends on the way the total current is divided among subbands.

Hall effect in quantum wires

Exact many-body eigenstates in a quantum dot formed in double-barrier heterostructures are calculated in the limit of strong confinement, and the nonlinear coherent transport through the states is studied for temperatures larger than their level broadenings. Energy splittings between many-body states due to exchange and correlation effects manifest themselves as small steps which decorate the Coulomb staircase in the current-voltage characteristics, which strongly depends on the number of electrons in the dot. Clear many-body effects are also found in peak heights and peak separations in the Coulomb oscillation of the linear conductance. \textcopyright{} 1996 The American Physical Society.

Many-body effects in transport through a quantum dot.

Connection rule of envelope functions at heterointerface

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