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Resonance phenomena in solids generally fall into two distinct classes, electric and magnetic, driven, respectively, by the $E$ and $H$ components of the electromagnetic wave incident on the solid. The canonical examples of the two types of resonances are the electron cyclotron resonance (CR) and the electron paramagnetic resonance (EPR), originating from the electron orbital and spin degrees of freedom, respectively. The behavior becomes considerably more interesting (and more complicated) in the presence of the spin-orbital interaction. In this case, a more general type of resonance may occur, which is driven by the electric excitation mechanism and involves the spin degrees of freedom. Such electric-dipole spin resonance (EDSR) may occur at the spin excitation frequency or at a combination of the orbital and spin frequencies, spanning a wide bandwidth. The EDSR phenomenon, first predicted by Rashba (1960), has been probed experimentally in 3D solids with different crystal symmetries, as well as in low-dimensional systems (heterojunctions, inversion layers, dislocations and impurity states). Due to its electric dipole origin, the EDSR features a relatively high intensity, which may exceed by orders of magnitude the EPR intensity. This review summarizes the work on EDSR prior to 1991, laying out the theoretical framework and discussing different experimental systems in which the EDSR-related physics can be realized and explored., Comment: published in: Landau Level Spectroscopy Edited by G. Landwehr and E.I. Rashba (Elsevier Science Publishers, 1991)

We introduce a solid-state qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gate-voltage pulses. We demonstrate two-axis control at a detuning sweet-spot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A {\pi}/2-gate time of 2.5 ns and a coherence time of 19 {\mu}s, using multi-pulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment.

We report initialization, complete electrical control, and single-shot readout of an exchange-only spin qubit. Full control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in under 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements, and non-orthogonal control axes., Comment: contains Supplementary Information

Graphene in spintronics has so far primarily meant spin current leads of high performance because the intrinsic spin-orbit coupling of its pi-electrons is very weak. If a large spin-orbit coupling could be created by a proximity effect, the material could also form active elements of a spintronic device such as the Das-Datta spin field-effect transistor, however, metal interfaces often compromise the band dispersion of massless Dirac fermions. Our measurements show that Au intercalation at the graphene-Ni interface creates a giant spin-orbit splitting (~100 meV) in the graphene Dirac cone up to the Fermi energy. Photoelectron spectroscopy reveals hybridization with Au-5d states as the source for the giant spin-orbit splitting. An ab initio model of the system shows a Rashba-split dispersion with the analytically predicted gapless band topology around the Dirac point of graphene and indicates that a sharp graphene-Au interface at equilibrium distance will account for only ~10 meV spin-orbit splitting. The ab initio calculations suggest an enhancement due to Au atoms that get closer to the graphene and do not violate the sublattice symmetry., Comment: 16 pages (3 figures) + supplementary information 16 pages (14 figures)

We study the energy spectrum of symmetric double quantum dots in narrow-gap carbon nanotubes with one and two electrostatically confined electrons in the presence of spin-orbit and Coulomb interactions. Compared to GaAs quantum dots, the spectrum exhibits a much richer structure because of the spin-orbit interaction that couples the electron's isospin to its real spin through two independent coupling constants. In a single dot, both constants combine to split the spectrum into two Kramers doublets, while the antisymmetric constant solely controls the difference in the tunneling rates of the Kramers doublets between the dots. For the two-electron regime, the detailed structure of the spin-orbit split energy spectrum is investigated as a function of detuning between the quantum dots in a 22-dimensional Hilbert space within the framework of a single-longitudinal-mode model. We find a competing effect of the tunneling and Coulomb interaction. The former favors a left-right symmetric two-particle ground state, while in the regime where the Coulomb interaction dominates over tunneling, a left-right antisymmetric ground state is found. As a result, ground states on both sides of the $(11)$-$(02)$ degeneracy point may possess opposite left-right symmetry, and the electron dynamics when tuning the system from one side of the $(11)$-$(02)$ degeneracy point to the other is controlled by three selection rules (in spin, isospin, and left-right symmetry). We discuss implications for the spin-dephasing and Pauli blockade experiments., Comment: revised version, accepted for publication in Phys. Rev. B

A recently discovered mechanism of electric dipole spin resonance, mediated by the hyperfine interaction, is investigated experimentally and theoretically. The effect is studied using a spin-selective transition in a GaAs double quantum dot. The resonant frequency is sensitive to the instantaneous hyperfine effective field, revealing a nuclear polarization created by driving the resonance. A device incorporating a micromagnet exhibits a magnetic field difference between dots, allowing electrons in either dot to be addressed selectively. An unexplained additional signal at half the resonant frequency is presented., Comment: Submitted as part of a SST special issue on spin-orbit effects in spintronics. Related papers at http://marcuslab.harvard.edu

We use charge sensing of Pauli blockade (including spin and isospin) in a two-electron 13C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time, T1, first decreases with parallel magnetic field then goes through a minimum in a field of 1.4 T. We attribute both results to the spin-orbit-modified electronic spectrum of carbon nanotubes, which suppresses hyperfine mediated relaxation and enhances relaxation due to soft phonons. The inhomogeneous dephasing time, T2*, is consistent with previous data on hyperfine coupling strength in 13C nanotubes., Comment: related papers at http://marcuslab.harvard.edu

An all-electrical spin resonance effect in a GaAs few-electron double quantum dot is investigated experimentally and theoretically. The magnetic field dependence and absence of associated Rabi oscillations are consistent with a novel hyperfine mechanism. The resonant frequency is sensitive to the instantaneous hyperfine effective field, and the effect can be used to detect and create sizable nuclear polarizations. A device incorporating a micromagnet exhibits a magnetic field difference between dots, allowing electrons in either dot to be addressed selectively., Comment: related papers available at http://marcuslab.harvard.edu

A theory of Electric Dipole Spin Resonance (EDSR), that is caused by various mechanisms of spin-orbit coupling, is developed as applied to free electrons in a parabolic quantum well. Choosing a parabolic shape of the well has allowed us to find explicit expressions for the EDSR intensity and its dependence on the magnetic field direction in terms of the basic parameters of the Hamiltonian. By using these expressions, we have investigated and compared the effect of specific mechanisms of spin orbit (SO) coupling and different polarizations of ac electric field on the intensity of EDSR. Angular dependences of the EDSR intensity are indicative of the relative contributions of the competing mechanisms of SO coupling. Our results show that electrical manipulating electron spins in quantum wells is generally highly efficient, especially by an in-plane ac electric field., Comment: 45 pages 6 figure

Electron spins in a semiconductor quantum well couple to an electric field {\it via} spin-orbit interaction. We show that the standard spin-orbit coupling mechanisms can provide extraordinary efficient electron spin manipulation by an in-plane ac electric field.

A theory of spin manipulation of quasi-two-dimensional (2D) electrons by a time-dependent gate voltage applied to a quantum well is developed. The Dresselhaus and Rashba spin-orbit coupling mechanisms are shown to be rather efficient for this purpose. The spin response to a perpendicular-to-plane electric field is due to a deviation from the strict 2D limit and is controlled by the ratios of the spin, cyclotron and confinement frequencies. The dependence of this response on the magnetic field direction is indicative of the strenghts of the competing spin-orbit coupling mechanisms.

Due to the spin-orbital coupling in a semiconductor quantum dot, a freely precessing electron spin produces a time-dependent charge density. This creates a sizeable electric field outside the dot, leading to promising applications in spintronics. The spin-electric coupling can be employed for non-invasive single spin detection by electrical methods. We also consider a spin relaxation mechanism due to long-range coupling to electrons in gates and elsewhere in the system, and find a contribution comparable to, and in some cases dominant over previously discussed mechanisms., Comment: 4 pages, 2 figures

Theory of electrical spin injection from a ferromagnetic (FM) metal into a normal (N) conductor is presented. We show that tunnel contacts (T) can dramatically increase spin injection and solve the problem of the mismatch in the conductivities of a FM metal and a semiconductor microstructure. We also present explicit expressions for the spin-valve resistance of FM-T-N- and FM-T-N-T-FM-junctions with tunnel contacts at the interfaces and show that the resistance includes both positive and negative contributions (Kapitza resistance and injection conductivity, respectively)., Comment: 4 pages, to appear in Phys. Rev. B (rapid communications)

Elementary excitations of incompressible quantum liquids (IQL's) are anyons, i.e., quasiparticles carrying fractional charges and obeying fractional statistics. To find out how the properties of these quasiparticles manifest themselves in the optical spectra, we have developed the anyon exciton model (AEM) and compared the results with the finite-size data for excitons of nu=1/3 and nu=2/3 IQL's. The model considers an exciton as a neutral composite consisting of three quasielectrons and a single hole. The AEM works well when the separation between electron and hole confinement planes, h, is larger than the magnetic length l. In the framework of the AEM an exciton possesses momentum k and two internal quantum numbers, one of which can be chosen as the angular momentum, L, of the k=0 state. Existence of the internal degrees of freedom results in the multiple branch energy spectrum, crater-like electron density shape and 120 degrees density correlations for k=0 excitons, and the splitting of the electron shell into bunches for non-zero k excitons. For h larger than 2l the bottom states obey the superselection rule L=3m (m are integers starting from 2), all of them are hard core states. For h nearly 2l there is one-to-one correspondence between the low-energy spectra found for the AEM and the many- electron exciton spectra of the nu=2/3 IQL, whereas some states are absent from the many-electron spectra of the nu=1/3 IQL. We argue that this striking difference in the spectra originates from the different populational statistics of the quasielectrons of charge conjugate IQL's and show that the proper account of the statistical requirements eliminates excessive states from the spectrum. Apparently, this phenomenon is the first manifestation of the exclusion statistics in the anyon bound states., Comment: 26 pages with 9 figures, typos corrected

We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems., Comment: RevTex, 18 pages, 5 ps fig

A theory of anyon excitons consisting of a valence hole and three quasielectrons with electric charges $(-e/3)$ is presented. A full symmetry classification of the $k=0$ states is given, where $k$ is the exciton momentum. The energy levels of these states are expressed by quadratures of confluent hypergeometric functions. It is shown that the angular momentum $L$ of the exciton ground state depends on the distance between electron and hole confinement planes and takes the values $L=3n$, where $n$ is an integer. With increasing $k$ the electron density shows a spectacular splitting on bundles. At first a single anyon splits off of the two-anyon core, and finally all anyons become separated., Comment: Revtex 13 pages + 6 uuencoded postscript figures