Abstract
Very recently, the electric dipole spin resonance (EDSR) of single electrons in quantum dots was discovered by three independent experimental groups. Remarkably, these observations revealed three different mechanisms of EDSR: coupling of electron spin to its momentum (spin-orbit), to the operator of its position (inhomogeneous Zeeman coupling), and to the hyperfine Overhauser field of nuclear spins. In this paper, I present a unified microscopic theory of these resonances in quantum dots. A mean field theory, derived for all three mechanisms and based on retaining only two-spin correlators, justifies applying macroscopic description of nuclear polarization to the EDSR theory. In the framework of the mean field theory, a fundamental difference in the time dependence of EDSR inherent of these mechanisms is revealed; it changes from the Rabi-type oscillations to a nearly monotonic growth. The theory provides a regular procedure to account for the higher nuclear-spin correlators that become of importance for a wider time span. For the hyperfine mechanism, they change the asymptotic behavior of EDSR dramatically. The theory also allows evaluating the effect of electron-spin dynamics on the effective coupling between nuclear spins.
Highlights
One of the principal avenues of semiconductor spintronics is based on the electrical manipulation of electron spins in single and double quantum dots that are envisioned as prospective blocks for quantum computation
Nowack et al.7 observed Rabi oscillations driven by the electric field generated by ac gate voltage and coupled to electron spin via the traditional spin-orbitSOinteraction
For an electron in a quantum dot, coupled to a nuclearspin reservoir by the hyperfine interaction, there exist at least three basic mechanisms of EDSR. They differ in the way the electron spin is coupled to ac electric field Et
Summary
One of the principal avenues of semiconductor spintronics is based on the electrical manipulation of electron spins in single and double quantum dots that are envisioned as prospective blocks for quantum computation. There are two major aspects of this problem. The main goals of the present paper areideriving mean field equations for three basic mechanisms of EDSR, ͑iideveloping efficient techniques for simplifying mean field integrals for spin-flip probability Wtand finding their asymptotic behavior at large t for various EDSR mechanisms, ͑iiideveloping a regular procedure for calculating corrections to the mean field results and establishing the time scale at which these corrections become essential and even critical, andivevaluating the effect of the forced precession of electron spin on the dynamics of nuclear bath The importance of these problems becomes more evident from the following arguments. Appendix B includes estimates of the corrections to mean field theory and proves that for the hyperfine EDSR mechanism they change the asymptotic behavior of Wtand become substantial at rather short times
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