Spin-orbit coupling and electron-phonon scattering - Fachbereich ...

4 Introduction
(phonons). Therefore, the electron-electron (e-e) and electron-phonon (e-p) interactions
set the limit for the observation of coherent phenomena in nanostructures
at low temperatures. On the other hand, the e-e interaction itself causes profound
effects like collective excitations of electrons, which in the parlance of many body
physics are called plasmons. The importance of e-e interaction is determined by
the electron density. In nanostructures the latter can be tuned by means of gates
voltages which may draw electrons from or to the system. With increasing electron
concentration the average kinetic energy is expected to become larger than
the average interaction energy. In this regime, many body effects can be neglected
and the electron is approximately a freely moving particle in an averaged background
potential caused by the other electrons. It is this approximation that we
shall apply throughout this work.
Similar to the phase information of a particle, the nature of its spin degree of
freedom is purely quantum mechanical. The fundamental issue of the influence
of the spin in electron transport has been a driving force in the field of magnetoelectronics
in the last decades [8]. The quantum nature of spin makes it inaccessible
to many of the dominating forces in a solid. Recently, this non-volatility
of spin has considerably sparked interest in the emerging field of spintronics [9],
which is an amalgamation of different areas in physics (electronics, photonics,
and magnetics). Being motivated by fundamental and applicational interests, the
paradigm of spintronics is either to add the spin degree of freedom to conventional
charge-based electronic devices, or to use the spin alone, aiming at the advantages
of its non-volatility. Such devices are expected to have an increased data processing
speed and integration density, and a decreased power consumption compared
to conventional semiconductor devices. From a very basic point of view, manipulating
the spin requires it to be distinguishable. This implies that the spin
degeneracy has to be lifted. Simple reasoning shows that single-particle states
of electrons in a solid are two-fold spin degenerate if time-reversal and spaceinversion
symmetry are simultaneously present. Thus, there are two generic ways
to address the spin: (i) Lift spin degeneracy by breaking time-reversal symmetry
by e.g. magnetic fields (external or internal as in the case of ferromagnets).
This corresponds to the magneto-electronic aspect of spintronics which has led to
e.g. the discovery of the giant magnetoresistance (GMR) effect in 1988 [10] that
is already employed in present-day hard disk drives. (ii) Lift spin degeneracy by
breaking space-inversion symmetry. In semiconductor nanostructures this leads
to the issue of spin-orbit coupling.
The relativistic coupling of spin and orbital motion is well known from atomic
physics in the context of fine-structure corrections to the spectrum of the hydrogen
atom. There, the effect of spin-orbit coupling can be estimated by the Sommerfeld
fine-structure constant α FS ≈ 1/137 as H SO /H 0 ≈ α 2 FS , being clearly a small
perturbation. On the contrary, in semiconductor nanostructures, the strength of