  Quantum transport in semiconductor nanostructures can be described
theoretically in terms of the propagation and scattering of electron
probability waves. Within this approach, elements of a phase-coherent electric
circuit play a role similar to quantum-optical devices that can be
characterised by scattering matrices. Electronic analogues of well-know optical
interferometers have been fabricated and used to study special features of
charge carriers in solids. We present results from our theoretical
investigation into the interplay between spin precession and quantum
interference in an electronic Mach-Zehnder interferometer with spin-orbit
coupling of the Rashba type. Intriguing spin-dependent transport effects occur,
which can be the basis for novel spintronic devices such as a magnet-less
spin-controlled field-effect transistor and a variety of single-qubit gates.
Their functionality arises entirely from spin-dependent interference of each
single input electron with itself. We have also studied two-electron
interference effects for the spin-dependent Mach-Zehnder interferometer,
obtaining analytical expressions for its two-fermion-state scattering matrix.
Using this result, we consider ways to generate two-electron output states for
which the Rashba spin-subband quantum number and the output-arm index are
entangled. Combining spin-dependent interference in our proposed Mach-Zehnder
interferometer with a projective charge measurement at the output enables
entanglement generation. As our particular scheme involves tuneable spin
precession, electric-field control of entanglement production can be achieved.

Mesoscale and Nanoscale Physics