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

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spindependent tunneling, as well as spin relaxation and spin dynamics The most fundamental spin-dependent nteraction in nonmagnetic semiconductors is spin-orbit coupling Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field

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Semiconductor Spintronics

Encyclopedia of Complexity and Systems Science

Semiconductor superlattices: a model system for nonlinear transport

Efficient Carbon Nanotube Photodiodes A single photon absorbed in a single-walled carbon nanotube device can generate multiple unbound particles carrying an electric charge. Gabor et al. (p. 1367) report that in such a device at low temperatures, excitation with light of increasing energy leads to well-defined stepwise increases in current. Interestingly, because of the unique band structure of carbon nanotubes, this behavior is analogous to particle-antiparticle creation commonly observed in high-energy particle physics. These observations point to the promise of investigations in other nanoscale carbon systems, such as graphene, and could lead to numerous applications, including highly sensitive photon detection and ultra-efficient photovoltaics. The decay of photoexcited electrons in a carbon nanotube device creates multiple pairs of charge carriers. We observed highly efficient generation of electron-hole pairs due to impact excitation in single-walled carbon nanotube p-n junction photodiodes. Optical excitation into the second electronic subband E22 leads to striking photocurrent steps in the device I-VSD characteristics that occur at voltage intervals of the band-gap energy EGAP/e. Spatially and spectrally resolved photocurrent combined with temperature-dependent studies suggest that these steps result from efficient generation of multiple electron-hole pairs from a single hot E22 carrier. This process is both of fundamental interest and relevant for applications in future ultra-efficient photovoltaic devices.

https://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/Gabor_Science_2009_supmat.pdf

Supporting Online Material for Extremely Efficient Multiple Electron-Hole Pair Generation in Carbon Nanotube Photodiodes

It is shown that the universal set of quantum logic gates can be realized using solid-state quantum bits based on coherent electron transport in quantum wires. The elementary quantum bits are realized with a proper design of two quantum wires coupled through a potential barrier. Numerical simulations show that (a) a proper design of the coupling barrier allows one to realize any one-qbit rotation and (b) Coulomb interaction between two qbits of this kind allows the implementation of the CNOT gate. These systems are based on a mature technology and seem to be integrable with conventional electronics.

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Quantum logic gates based on coherent electron transport in quantum wires.

We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the linear entropy used to treat quantum entanglement in systems of nonidentical particles. Such a criterion is here applied to an electron-electron scattering in a two-dimensional system in order to perform a quantitative evaluation of the entanglement dynamics for various spin configurations and to compare the linear entropy with alternative approaches. Our numerical results show the dependence of the entanglement evolution upon the initial state of the system and its spin components. The differences with previous analyses accomplished by using the von Neumann entropy are discussed. The evaluation of the entanglement dynamics in terms of the linear entropy results to be much less demanding from the computational point of view, not requiring the diagonalization of the density matrix.

https://arxiv.org/pdf/quant-ph/0611223.pdf

Linear entropy as an entanglement measure in two-fermion systems

A theoretical Wigner-function approach to the study of quantum transport in open systems in presence of phonon scattering is presented. It is shown here that in order to solve the Wigner equation in its integral form the knowledge of the Wigner function at all points of the phase space at an initial time ${t}_{0}$ can be substituted by the knowledge of the same function inside the region of interest at ${t}_{0}$ and on its boundary at all times ${t}^{\ensuremath{'}}$ less then the observation time $t.$ The theory has been applied to calculate the current associated with electron quantum transport across given potential profiles and in presence of phonon scattering.

Quantum transport of electrons in open nanostructures with the wigner-function formalism

The coherent dynamics of carriers bound to bent cylindrical surfaces is modeled by numerically solving the open-boundary Schr\"odinger equation recast in surface curvilinear coordinates. The effect of the surface topology on the transmission properties is addressed for bent cylinders and smooth junctions of cylinders with different radii. It is shown that, where the curvature changes sharply, quantum interference phenomena are induced, leading to an oscillatory behavior of the transmission coefficient as a function of the geometrical parameters. The spectra of bound states are also computed. The analysis has been carried out using the geometrical and physical parameters of carbon nanotubes, whose topology can be modeled, in many significant cases, using the presented approach.

Coherent electron transport in bent cylindrical surfaces

Free-standing semiconductor nanowires in combination with advanced gate-architectures hold an exceptional promise as miniaturized building blocks in future integrated circuits. However, semiconductor nanowires are often corrupted by an increased number of close-by surface states, which are detrimental with respect to their optical and electronic properties. This conceptual challenge hampers their potentials in high-speed electronics and therefore new concepts are needed in order to enhance carrier mobilities. We have introduced a novel type of core–shell nanowire heterostructures that incorporate modulation or remote doping and hence may lead to high-mobility electrons. We demonstrate the validity of such concepts using inelastic light scattering to study single modulation-doped GaAs/Al0.16Ga0.84As core-multishell nanowires grown on silicon. We conclude from a detailed experimental study and theoretical analysis of the observed spin and charge density fluctuations that one- and two-dimensional electron ch...

Andrea Bertoni

Papers

Quantum logic gates based on coherent electron transport in quantum wires.

Linear entropy as an entanglement measure in two-fermion systems

Quantum transport of electrons in open nanostructures with the wigner-function formalism

Coherent electron transport in bent cylindrical surfaces

High Mobility One- and Two-Dimensional Electron Systems in Nanowire-Based Quantum Heterostructures