Correlated spin transport in nanostructures: entanglement creation and spin filtering

The electron spin for electronics has only recently attracted much interest.
The idea to use spin|as opposed to charge|as the fundamental data carrier
was motivated by recent experiments that showed unusually long spindephasing
times up to microseconds for electrons in semiconductors as well
as phase coherent transport over distances exceeding one hundred micrometers.
In addition, experiments demonstrated the injection of spin-polarized
carriers|electrons and holes|from a magnetic into a non-magnetic semiconductor
which opens the door for various applications in spin electronics
(spintronics). Besides the broad use of the electron spin in conventional devices,
like in giant magnetoresistance (GMR) based magnetic read-out heads
for computer hard drives or for non-volatile memories, the spin of the electron
con�ned in nanostructures such as semiconductor quantum dots serves
as a natural realization of a quantum bit (qubit). A quantum computer
uses explicitly the quantum nature of systems where phase coherence and
entanglement play a crucial role which requires a radically new design of
the underlying computer hardware. In particular, entangled spin qubits,
combined with the ability to control them via their charges, can serve as
electronic EPR (Einstein-Podolsky-Rosen)-pairs in wires, i.e. pairs of electrons
which are spatially separated (and uncorrelated) but still correlated
with respect to their spins. Such entangled particles are the resource for
secure quantum communication protocols which have been experimentally
implemented using photons|the quantized units of light. The equivalent
experiments for massive particles like electrons in a solid-state environment
have not yet been performed, although their need cannot be overestimated,
both from a practical point of view and also from a more fundamental one.
In this Thesis, we address the question of creating such nonlocal spinentangled
electron pairs in a way that is suitable to detect the produced entanglement
in transport experiments via their current-noise properties. We discuss various setups|entanglers| where Cooper pairs in a superconductor
with spin singlet wave functions act as the source of spin-entanglement. In
the presence of a voltage bias between the superconductor and two spatially
separated normal conducting leads which are weakly tunnel-coupled to the
superconductor, the electrons of a Cooper pair can tunnel coherently|in an
Andreev (pair-)tunneling process|from the superconductor to the normal
leads thereby remaining in the spin singlet state. This produces a current
carried by pairs of spin-entangled electrons in the leads. In these setups,
superconducting pair-correlations and Coulomb interaction between the two
electrons are competing features. On the one hand, the orbital wave function
of a Cooper pair is symmetric which favors the tunneling of both electrons
into the same outgoing arm of the entangler. Such processes are unwanted
since they do not lead to nonlocality. On the other hand, in small lowdimensional
quantum con�ned nanostructres, electron-electron interaction
becomes sizable and can be used to separate the two electrons of a Cooper
pair. We exploit such strong correlations between the electron charges of
a pair by using either quantum dots in the Coulomb blockade regime, one
dimensional wires with Luttinger liquid properties or resistive outgoing leads
coupled to the superconductor. We calculate the two competing tunneling
currents from the superconductor to di�erent leads (desired pair-split process)
and to the same lead (unwanted local process) in detail. By comparing
their ratio, we can estimate the e�ciency of the entangler and see how it
depends on various system parameters. This then allows us to identify a
regime of experimental accessibility where the pair-split process is dominant.
The ability to have (coherent) control over single electron spins in semiconductor
nanostructures is crucial in view of quantum computing with electron
spins. In particular, spin-�ltering and spin read-out is of great importance.
For this we consider a quantum dot in the Coulomb blockade regime
weakly coupled to current leads and show that in the presence of a magnetic
�eld the dot acts as an e�cient spin �lter (at the single-spin level) which
produces a spin-polarized current. Conversely, if the leads are fully spinpolarized,
the magnitude of the transport current through the dot depends
on the spin state of the dot. Quantum dots permit the control of charge
down to single electrons. It is therefore feasible to consider a single spin 1/2
on the dot|a spin qubit|which can be read out by a current. Combined
with electron spin resonance (ESR) techniques this allows one to operate the
quantum dot as a single spin memory with read-in and read-out capabilities.